ML Aggarwal Class 8 Maths Solutions Chapter 08 Simple and Compound Interest

Exercise 8.1

Question 1. Find the simple interest on Rs 4000 at 7.5% p.a. for 3 years 3 months. Also, find the amount.
Answer: The principal is Rs 4000, the rate is 7.5% per annum (or 15/2 % p.a.), and the time is 3 years 3 months which equals 13/4 years. Using the simple interest formula I = (P × R × T) / 100, we get I = (4000 × 15/2 × 13/4) / 100 = Rs 975. The amount is calculated by adding the principal and interest: Amount = P + I = Rs 4000 + Rs 975 = Rs 4975.
In simple words: When you put Rs 4000 in a bank at 7.5% interest for 3 years 3 months, you earn Rs 975 as interest, so your total becomes Rs 4975.

Exam Tip: Always convert mixed time periods (like 3 years 3 months) into a single fraction of years before applying the simple interest formula - this prevents calculation errors.

Question 2. What sum of money will yield Rs 170.10 as simple interest in 2 years 3 months at 6% per annum?
Answer: Here the simple interest earned is Rs 170.10, the rate is 6% p.a., and the time is 2 years 3 months which equals 9/4 years. To find the principal, we use the formula P = (I × 100) / (R × T) = (170.10 × 100) / (6 × 9/4) = (170.10 × 100 × 4) / (6 × 9) = Rs 1260. Therefore, the sum of money needed is Rs 1260.
In simple words: If someone earned Rs 170.10 as interest over 2 years 3 months at 6% per year, they must have put in Rs 1260 to start with.

Exam Tip: When finding the principal from interest, remember to rearrange the simple interest formula correctly - multiply by 100 and divide by both rate and time.

Question 3. Find the rate of interest when Rs 800 fetches Rs 130 as a simple interest in 2 years 6 months.
Answer: The principal is Rs 800, the simple interest is Rs 130, and the time is 2 years 6 months which equals 5/2 years. Using the formula R = (I × 100) / (P × T), we get R = (130 × 100) / (800 × 5/2) = (130 × 100 × 2) / (800 × 5) = 6.5% p.a. So the rate of interest is 6.5% per annum.
In simple words: A principal of Rs 800 that earns Rs 130 in 2 years 6 months is getting 6.5% interest each year.

Exam Tip: When solving for rate, be careful with fraction division - convert the time to a single fraction first and multiply by its reciprocal when cross-multiplying.

Question 4. Find the time when simple interest on Rs 3.3 lakhs at 6.5% per annum is Rs 75075.
Answer: The principal is 3.3 lakhs which equals Rs 330000, the rate is 6.5% p.a., and the simple interest is Rs 75075. Using the formula T = (I × 100) / (P × R), we get T = (75075 × 100) / (330000 × 6.5) = (75075 × 100 × 10) / (330000 × 65) = 7/2 years = 3 years 6 months. Therefore, the time period is 3 years 6 months.
In simple words: If Rs 330000 earns Rs 75075 at 6.5% interest, it takes 3 years 6 months to earn that amount.

Exam Tip: Convert large numbers like "3.3 lakhs" to standard rupees before using the formula, and express the final answer back in years and months for clarity.

Question 5. Find the sum of money when (i) simple interest at 7.25% p.a. for 2.5 years is Rs 2356.25 (ii) the final amount is Rs 11300 at 4% p.a. for 3 years 3 months.
Answer:
(i) The simple interest is Rs 2356.25, the rate is 7.25% (or 29/4 % p.a.), and the time is 2.5 years (or 5/2 years). Using P = (I × 100) / (R × T), we get P = (2356.25 × 100) / (29/4 × 5/2) = (2356.25 × 100 × 4 × 2) / (29 × 5) = Rs 13000. So the principal is Rs 13000.
(ii) The amount is Rs 11300, the rate is 4% p.a., and the time is 3 years 3 months which equals 13/4 years. Let the principal be x. Simple Interest = (x × 4 × 13) / (100 × 4) = 13x/100. Amount = x + 13x/100 = 113x/100. Since the amount is Rs 11300, we have 113x/100 = 11300, so x = 10000. Therefore, the principal is Rs 10000.
In simple words: In part (i), if the interest earned is Rs 2356.25 at 7.25% for 2.5 years, you started with Rs 13000. In part (ii), if the final amount is Rs 11300 at 4% for 3 years 3 months, the original sum was Rs 10000.

Exam Tip: For part (ii), set up the amount equation carefully - amount equals principal plus interest, and use this to solve for the unknown principal algebraically.

Question 6. How long will it take a certain sum of money to triple itself at 13.33% per annum simple interest?
Answer: Let the sum be x. When it triples, the amount becomes 3x, so the simple interest earned is 3x - x = 2x. The rate is 13.33% (or 40/3 % p.a.). Using the formula T = (I × 100) / (P × R), we get T = (2x × 100) / (x × 40/3) = (2 × 100 × 3) / 40 = 15 years. Therefore, it will take 15 years for the sum to triple.
In simple words: At 13.33% simple interest per year, any amount of money will become three times bigger in 15 years.

Exam Tip: When dealing with "triple itself" problems, remember that the interest earned equals 2 times the principal (since final amount = 3 × principal).

Question 7. At a certain rate of simple interest Rs 4050 amounts to Rs 4576.50 in 2 years. At the same rate of simple interest, how much would Rs 1 lakh amount to in 3 years?
Answer: First, we find the rate of interest. The principal is Rs 4050, the amount is Rs 4576.50, and the time is 2 years. Interest = Rs 4576.50 - Rs 4050 = Rs 526.50. Using R = (I × 100) / (P × T), we get R = (526.50 × 100) / (4050 × 2) = 6.5% p.a. Now, for Rs 1 lakh (Rs 100000) at 6.5% p.a. for 3 years, the interest is I = (100000 × 6.5 × 3) / 100 = Rs 19500. Therefore, the amount = Rs 100000 + Rs 19500 = Rs 119500.
In simple words: First figure out the interest rate from the first situation (6.5%), then use that same rate to find how much Rs 100000 will grow to in 3 years, which is Rs 119500.

Exam Tip: Two-part interest problems require you to find the rate from the first situation, then apply it to a different principal and time in the second part.

Question 8. What sum of money invested at 7.5% p.a. simple interest for 2 years produces twice as much interest as Rs 9600 in 3 years 6 months at 10% p.a. simple interest?
Answer: First, we calculate the interest from the first case: Principal = Rs 9600, Rate = 10% p.a., Time = 3 years 6 months = 7/2 years. Interest = (9600 × 10 × 7) / (100 × 2) = Rs 3360. In the second case, the required interest is twice this amount = Rs 6720. Now, we find the principal needed to produce Rs 6720 at 7.5% p.a. for 2 years. Using P = (I × 100) / (R × T), we get P = (6720 × 100) / (7.5 × 2) = Rs 44800. Therefore, the sum to be invested is Rs 44800.
In simple words: Rs 9600 at 10% for 3.5 years gives Rs 3360 interest. To get double that interest (Rs 6720) at 7.5% for 2 years, you need to invest Rs 44800.

Exam Tip: In "twice as much interest" problems, calculate the first interest, multiply by 2, then use that result as the interest in the principal formula.

Exercise 8.2

Question 1. Calculate the compound interest on Rs 6000 at 10% per annum for two years.
Answer: The principal is Rs 6000 and the rate is 10% p.a. For the first year, interest = (6000 × 10 × 1) / 100 = Rs 600. Amount at the end of first year = Rs 6000 + Rs 600 = Rs 6600. This amount becomes the principal for the second year. For the second year, interest = (6600 × 10 × 1) / 100 = Rs 660. Amount at the end of second year = Rs 6600 + Rs 660 = Rs 7260. Compound interest for 2 years = Rs 7260 - Rs 6000 = Rs 1260.
In simple words: Year 1 gives you Rs 600 interest, making your total Rs 6600. Year 2 gives you Rs 660 interest on this new amount, making your final total Rs 7260. So you earned Rs 1260 extra over 2 years.

Exam Tip: In compound interest, always remember that the interest for each year becomes part of the principal for the next year - this is what makes it "compound".

Question 2. Salma borrowed from Mahila Samiti a sum of Rs 1875 to purchase a sewing machine. If the rate of interest is 4% per annum, what is the compound interest that she has to pay after 2 years?
Answer: The principal is Rs 1875 and the rate is 4% p.a. For the first year, interest = (1875 × 4 × 1) / 100 = Rs 75. Amount at the end of first year = Rs 1875 + Rs 75 = Rs 1950. For the second year, interest = (1950 × 4 × 1) / 100 = Rs 78. Amount at the end of second year = Rs 1950 + Rs 78 = Rs 2028. Compound interest Salma must pay = Rs 2028 - Rs 1875 = Rs 153.
In simple words: After 2 years of borrowing Rs 1875 at 4% interest, Salma will have earned Rs 75 in the first year and Rs 78 in the second year, for a total extra amount of Rs 153 that she has to pay back.

Exam Tip: For real-life borrowing problems, clearly show the year-by-year working and make sure the final answer is the compound interest, not the total amount due.

Question 3. Jacob invests Rs 12000 for 3 years at 10% per annum. Calculate the amount and the compound interest that Jacob will get after 3 years.
Answer: The principal is Rs 12000 and the rate is 10% p.a. For the first year, interest = (12000 × 10 × 1) / 100 = Rs 1200. Amount at end of first year = Rs 13200. For the second year, interest = (13200 × 10 × 1) / 100 = Rs 1320. Amount at end of second year = Rs 14520. For the third year, interest = (14520 × 10 × 1) / 100 = Rs 1452. Amount at end of third year = Rs 15972. Compound interest = Rs 15972 - Rs 12000 = Rs 3972.
In simple words: Jacob's Rs 12000 grows year by year - first to Rs 13200, then to Rs 14520, finally to Rs 15972. The total interest earned is Rs 3972.

Exam Tip: For 3-year problems, organize your work in three clear rows (one per year) showing principal, interest, and new amount - this prevents mistakes.

Question 4. A man invests Rs 46875 at 4% per annum compound interest for 3 years. Calculate: (i) the interest for the first year (ii) the amount standing to his credit at the end of second year (iii) the interest for the third year
Answer:
(i) Principal for the first year = Rs 46875. Interest for the first year = (46875 × 4 × 1) / 100 = Rs 1875.
(ii) Amount at the end of first year = Rs 46875 + Rs 1875 = Rs 48750. Principal for second year = Rs 48750. Interest for second year = (48750 × 4 × 1) / 100 = Rs 1950. Amount at end of second year = Rs 48750 + Rs 1950 = Rs 50700.
(iii) Principal for third year = Rs 50700. Interest for third year = (50700 × 4 × 1) / 100 = Rs 2028.
In simple words: Year 1 earns Rs 1875 interest. By the end of Year 2, the total amount is Rs 50700. In Year 3, the interest earned is Rs 2028, which is more than Year 1 because the principal has grown.

Exam Tip: When a multi-part question asks for different things (interest in one year, amount at a different point, interest in another year), make sure you answer exactly what is asked in each part.

Question 5. Calculate the compound interest for the second year on Rs 6000 invested for 3 years at 10% p.a. Also find the sum due at the end of third year.
Answer: The principal is Rs 6000 and the rate is 10% p.a. For the first year, interest = (6000 × 10 × 1) / 100 = Rs 600. Amount at end of first year = Rs 6600. For the second year, interest = (6600 × 10 × 1) / 100 = Rs 660. Amount at end of second year = Rs 7260. For the third year, interest = (7260 × 10 × 1) / 100 = Rs 726. Amount at end of third year = Rs 7986. The compound interest for the second year is Rs 660, and the sum due at the end of third year is Rs 7986.
In simple words: The second year's interest alone is Rs 660. By the end of year 3, the total amount grows to Rs 7986.

Exam Tip: Be careful to distinguish between "interest earned in a particular year" (just that year's interest) and "sum due at the end of a year" (the full accumulated amount).

Question 6. Calculate the amount and the compound interest on Rs 5000 in 2 years when the rate of interest for successive years is 6% and 8% respectively.
Answer: The principal is Rs 5000. For the first year at 6% rate, interest = (5000 × 6 × 1) / 100 = Rs 300. Amount at end of first year = Rs 5300. For the second year at 8% rate, interest = (5300 × 8 × 1) / 100 = Rs 424. Amount at end of second year = Rs 5724. Compound interest for two years = Rs 5724 - Rs 5000 = Rs 724.
In simple words: When rates change year to year, apply each rate to that year's principal. First year at 6% gives Rs 300 interest, second year at 8% gives Rs 424 interest, for a total of Rs 724.

Exam Tip: When rates change year by year, always use the correct rate for each year - never average them or apply the same rate to all years.

Question 7. Calculate the difference between the compound interest and the simple interest on Rs 20000 in 2 years at 8% per annum.
Answer: For simple interest: S.I. = (20000 × 8 × 2) / 100 = Rs 3200. For compound interest: Amount = 20000 {1 + (8/100)}² = 20000 × (27/25) × (27/25) = 20000 × (729/625) = Rs 23328. Compound interest = Rs 23328 - Rs 20000 = Rs 3328. Difference = Rs 3328 - Rs 3200 = Rs 128. The compound interest is Rs 128 more than the simple interest.
In simple words: At 8% for 2 years, simple interest gives you Rs 3200 extra, but compound interest gives you Rs 3328 extra. The difference is Rs 128 - that extra comes from earning interest on your interest.

Exam Tip: When comparing simple and compound interest, remember that compound interest is always equal to or greater than simple interest - the difference grows larger for longer time periods and higher rates.

Exercise 8.3

Question 1. Calculate the amount and compound interest on (i) Rs 15000 for 2 years at 10% per annum compounded annually. (ii) Rs 156250 for 1.5 years at 8% per annum compounded half-yearly. (iii) Rs 100000 for 9 months at 4% per annum compounded quarterly.
Answer:
(i) Principal = Rs 15000, Rate = 10% p.a., Period = 2 years. Amount = 15000 {1 + (10/100)}² = 15000 × (11/10) × (11/10) = Rs 18150. Compound interest = Rs 18150 - Rs 15000 = Rs 3150.
(ii) Principal = Rs 156250, Rate = 8% p.a. or 4% half-yearly, Period = 1.5 years = 3 half-years. Amount = 156250 {1 + (4/100)}³ = 156250 × (26/25)³ = 156250 × (26/25) × (26/25) × (26/25) = Rs 175760. Compound interest = Rs 175760 - Rs 156250 = Rs 19510.
(iii) For this sub-part, the solution in the source PDF is incomplete. Principal = Rs 100000, Rate = 4% p.a. or 1% quarterly, Period = 9 months = 3 quarters. Amount = 100000 {1 + (1/100)}³ = 100000 × (101/100)³ = 100000 × (101/100) × (101/100) × (101/100) = Rs 103030.301. Compound interest = Rs 3030.301 (approximately Rs 3030.30).
In simple words: Part (i): Rs 15000 grows to Rs 18150 when compounded yearly at 10% for 2 years. Part (ii): Rs 156250 grows to Rs 175760 when interest is added twice a year (half-yearly) at 8% for 1.5 years. Part (iii): Rs 100000 grows when interest is added four times a year (quarterly) at 4% for 9 months.

Exam Tip: When compounding happens more than once a year (half-yearly or quarterly), divide the annual rate by the number of periods and multiply the time in years by the same number to get the total number of compounding periods.

Question 2. Find the difference between the simple interest and compound interest on Rs 4800 for 2 years at 5% per annum, compound interest being reckoned annually.
Answer: For simple interest: S.I. = (4800 × 5 × 2) / 100 = Rs 480. For compound interest: Amount = 4800 {1 + (5/100)}² = 4800 × (21/20) × (21/20) = Rs 5292. Compound interest = Rs 5292 - Rs 4800 = Rs 492. Difference = Rs 492 - Rs 480 = Rs 12. The compound interest exceeds simple interest by Rs 12.
In simple words: At 5% for 2 years on Rs 4800, simple interest gives Rs 480 while compound interest gives Rs 492. The difference is Rs 12 extra money earned through compound interest.

Exam Tip: The difference between CI and SI is relatively small for short periods and low rates, but it grows significantly for longer periods and higher rates.

Question 3. Find the compound interest on Rs 3125 for 3 years if the rates of interest for the first, second and third year are respectively 4%, 5% and 6% per annum.
Answer: The principal is Rs 3125. The rates for each year are different: 4%, 5%, and 6%. Amount = 3125 {1 + (4/100)} {1 + (5/100)} {1 + (6/100)} = 3125 × (26/25) × (21/20) × (53/50) = 3125 × (26 × 21 × 53) / (25 × 20 × 50) = Rs 3617.25. Compound interest = Rs 3617.25 - Rs 3125 = Rs 492.25.
In simple words: When the interest rate changes each year, multiply the principal by (1 + rate/100) for each year separately, rather than using an exponent. This gives Rs 3617.25 at the end, earning Rs 492.25 in compound interest.

Exam Tip: For varying rates, never try to average the rates - instead, apply each rate individually in sequence to get the correct final amount.

Question 4. Kamla borrowed Rs 26400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?
Answer: The principal is Rs 26400, the rate is 15% p.a., and the time is 2 years and 4 months = 2 years + 4/12 years = 2 years + 1/3 year = 7/3 years. For 2 complete years, Amount = 26400 {1 + (15/100)}² = 26400 × (23/20) × (23/20) = 26400 × (529/400) = Rs 34914. For the remaining 4 months (1/3 year), we apply simple interest on Rs 34914: Interest = (34914 × 15 × 1/3) / 100 = Rs 1745.70. Total amount = Rs 34914 + Rs 1745.70 = Rs 36659.70.
In simple words: For 2 full years, the amount grows with compound interest. For the remaining 4 months, we add simple interest on that new amount. The final total Kamla must pay is Rs 36659.70.

Exam Tip: When the time period includes a fraction of a year, use compound interest for complete years and simple interest for the remaining fraction.

Question 5. Anil borrowed Rs 18000 from Rakesh at 8% per annum simple interest for 2 years. If Anil had borrowed this sum at 8% per annum compound interest, what extra amount would he has to pay?
Answer: For simple interest: S.I. = (18000 × 8 × 2) / 100 = Rs 2880. For compound interest: Amount = 18000 {1 + (8/100)}² = 18000 × (27/25) × (27/25) = 18000 × (729/625) = Rs 20995.20. Compound interest = Rs 20995.20 - Rs 18000 = Rs 2995.20. Extra amount = Rs 2995.20 - Rs 2880 = Rs 115.20. Anil would have to pay Rs 115.20 extra if compound interest were applied.
In simple words: With simple interest, Anil pays back Rs 2880 in interest. With compound interest, he pays Rs 2995.20 in interest. The extra amount due to compound interest is Rs 115.20.

Exam Tip: To find "extra amount", calculate both SI and CI separately, then subtract SI from CI - this shows the extra charge for using compound interest.

Question 6. Mukesh borrowed Rs 75000 from a bank. If the rate of interest is 12% per annum, find the amount he would be paying after 1\( \frac{1}{2} \) years if the interest is (i) compounded annually (ii) compounded half-yearly
Answer: When interest is compounded yearly: Rs 75000 at 12% per annum for 1\( \frac{1}{2} \) years gives an amount of Rs 89040. The calculation involves multiplying the principal by the growth factor \( (28/25) \) for the first year and \( (53/50) \) for the next half year.
When interest is compounded half-yearly: The principal grows at 6% per half-year (since 12% ÷ 2 = 6%) for 3 half-year periods. The amount works out to Rs 89326.20, using the growth factor \( (53/50) \) applied three times.
In simple words: Compound interest means the interest you earn also earns more interest. When the bank compounds it yearly, you get Rs 89040. When they compound it every six months instead, you get a bit more - Rs 89326.20 - because your money starts earning interest sooner.

Exam Tip: Always convert the annual rate to the half-yearly rate by dividing by 2, and double the time period when interest is compounded half-yearly. Check that your final amount is higher with half-yearly compounding than with annual compounding.

Question 7. Aryaman invested Rs 10000 in a company, he would be paid interest at 7% per annum compounded annually. Find (i) the amount received by him at the end of 2 years (ii) the interest for the 3rd year
Answer: (i) Using the compound interest formula, the principal of Rs 10000 grows at 7% per year. After 2 years, multiplying the principal by \( (107/100) \) twice gives Rs 11449.
(ii) For the 3rd year, first calculate the amount after 3 years by multiplying Rs 11449 by \( (107/100) \), which equals Rs 12250.43. The interest earned in the 3rd year alone is the difference between the amount after 3 years and the amount after 2 years: Rs 12250.43 - Rs 11449 = Rs 801.43.
In simple words: After 2 years, your Rs 10000 becomes Rs 11449 because it grew by 7% each year. In just the 3rd year alone, you earn Rs 801.43 in interest - more than in earlier years because the interest itself has been growing.

Exam Tip: To find interest for a specific year, always calculate the amount at the end of that year and subtract the amount at the start of that year. The interest grows each year because you earn interest on interest.

Question 8. What sum of money will amount to Rs 9261 in 3 years at 5% per annum compound interest?
Answer: Using the compound interest formula rearranged to find the principal: If the final amount is Rs 9261 after 3 years at 5% per annum, then the principal can be found by dividing the amount by \( (1 + 5/100)^3 \). This equals Rs 9261 ÷ \( (21/20)^3 \) = Rs 9261 × \( (20/21)^3 \). Multiplying out gives Rs 8000.
In simple words: You need to work backwards from the final amount. If Rs 8000 grows to Rs 9261 in 3 years at 5% compound interest, then Rs 8000 is the starting amount you must invest.

Exam Tip: When finding the principal, rearrange the formula to P = A / {1 + (r/100)}^n. Always verify by multiplying your answer back: Rs 8000 × (1.05)^3 should equal Rs 9261.

Question 9. What sum invested for 1\( \frac{1}{2} \) years compounded half-yearly at the rate of 8% p.a. will amount to Rs 140608?
Answer: The annual rate of 8% becomes 4% per half-year. Over 1\( \frac{1}{2} \) years, there are 3 half-year periods. Rearranging the compound interest formula: Principal = Amount ÷ \( (1 + 4/100)^3 \) = Rs 140608 ÷ \( (26/25)^3 \). Computing the division yields a principal of Rs 125000.
In simple words: To find how much you need to invest, divide the final amount by the growth factor. Here, Rs 140608 divided by the growth over 3 half-year periods equals Rs 125000.

Exam Tip: Always halve the annual rate and double the time period when interest is compounded half-yearly. This keeps the number of compounding periods consistent with the rate used.

Question 10. At what rate percent will Rs 2000 amount to Rs 2315.25 in 3 years at compound interest?
Answer: Set up the equation: \( (1 + r/100)^3 = 2315.25 / 2000 \) = \( 9261/8000 \) = \( (21/20)^3 \). Since both sides are cubes, taking the cube root gives \( 1 + r/100 = 21/20 \). Therefore \( r/100 = 1/20 \), which means \( r = 5 \). The rate of interest is 5% per annum.
In simple words: The amount grew to 1.05 times the original in 3 years. This growth happens when money increases by 5% each year. So the rate must be 5%.

Exam Tip: When solving for rate, try to express the ratio as a perfect power (in this case, a cube) of a simple fraction. This makes finding the rate straightforward.

Question 11. If Rs 40000 amounts to Rs 46305 in 1\( \frac{1}{2} \) years, compound interest payable half-yearly, find the rate of interest per annum.
Answer: Since interest is compounded half-yearly, the time period of 1\( \frac{1}{2} \) years equals 3 half-year periods. Set up: \( (1 + r/100)^3 = 46305 / 40000 \) = \( 9261/8000 \) = \( (21/20)^3 \). Taking cube roots: \( 1 + r/100 = 21/20 \), so \( r/100 = 1/20 \), giving \( r = 5 \). This is the rate per half-year. The annual rate is 5% × 2 = 10% per annum.
In simple words: The money grew in 3 half-year periods, so the interest rate you calculate (5%) applies to each half-year. To get the yearly rate, multiply by 2, giving 10% per annum.

Exam Tip: Remember that when interest is compounded half-yearly, the rate you find from the equation is for the half-year period. Always double it to get the annual rate.

Question 12. In what time will Rs 15625 amount to Rs 17576 at 4% per annum compound interest?
Answer: Using the compound interest formula: \( 17576 / 15625 = (1 + 4/100)^n \) = \( (26/25)^n \). Computing the left side: \( 17576/15625 = (26/25)^3 \). Since the bases match, \( n = 3 \). The time period is 3 years.
In simple words: Divide the final amount by the starting amount to get the growth ratio. If this ratio equals (26/25) multiplied by itself 3 times, then 3 years have passed.

Exam Tip: Express both sides of the equation as powers of the same base. If you can match the exponents, you have found the time period directly.

Question 13. Rs 16000 invested at 10% p.a. compounded semi-annually, amounts to Rs 18522. Find the time period of investment.
Answer: The annual rate of 10% becomes 5% per half-year. Set up the equation: \( 18522 / 16000 = (1 + 5/100)^n \), where n is in half-year periods. Simplifying: \( 9261/8000 = (21/20)^n \). Since \( (21/20)^3 = 9261/8000 \), we have \( n = 3 \) half-years. Converting to years: 3 half-years = 3/2 = 1\( \frac{1}{2} \) years.
In simple words: When interest compounds every six months, count time in half-year blocks. Here, 3 half-year periods pass, which equals 1.5 or 1\( \frac{1}{2} \) years total.

Exam Tip: Always work in the compounding period (half-years here, not full years). Find n in those units, then convert back to years by dividing by the number of half-years per year (which is 2).