Q: ₹800 at 5% per annum compounded annually will amount to ₹882 in how many years?

2 year. For annual compounding, the amount is $A=P(1+r/100)^n$. Here $882=800(1.05)^n$, so $882/800=1.1025=(1.05)^2$. Hence, $n=2$ years.

Q: If the rate of interest is 4% per annum for the first year, 5% per annum for the second year, and 6% per annum for the third year, then the compound interest on ₹10000 for 3 years will be:

₹1575.20. With varying annual rates, the amount becomes $10000\times1.04\times1.05\times1.06=11575.20$. Subtracting the principal gives compound interest $=11575.20-10000=1575.20$.

Q: The compound interest on ₹8000 at 15% per annum for 2 years 4 months, when compounded annually, is:

₹3109. For annual compounding, first compound for 2 years: $8000(1.15)^2=10580$. For the remaining 4 months, take simple interest on this amount: $10580\times15\%\times\frac{4}{12}=529$. Total CI = $10580-8000+529=3109$.

Q: A certain amount of money earns ₹540 as simple interest in 3 years. If it earns compound interest of ₹376.20 at the same rate of interest in 2 years, find the principal amount (in ₹).

2000. From simple interest, $P\times r\times 3/100=540$, so $Pr=18000$. For 2 years, $CI-SI=\frac{Pr^2}{10000}$. Using $CI=376.20$ and $SI=\frac{Pr\times2}{100}=360$, the difference is $16.20$, which gives $P=2000$.

Q: The compound interest on a certain sum of money invested for 2 years at 5% per annum is ₹328. The simple interest on the sum, at the same rate and for the same period, will be:

₹320. For 2 years at rate $r$, $CI-SI=\frac{Pr^2}{10000}$. Here $CI=328$ and $r=5\%$, so the difference is $P\times25/10000=0.0025P$. Solving gives $P=3200$, and hence $SI=\frac{3200\times5\times2}{100}=320$.

Question 1

The compound interest on ₹12,000 for 9 months at 20% per annum, interest being compounded quarterly, is:

Accepted Answer

₹1891.50. At 20% per annum compounded quarterly, the rate per quarter is 5%. In 9 months, there are 3 quarters. Amount = 12000(1.05)^3 = 13891.50, so compound interest = 13891.50 - 12000 = ₹1891.50.

Question 2

In what time will ₹64,000 amount to ₹68,921 at 5% per annum, interest being compounded half-yearly?

Accepted Answer

1 year 6 months. With half-yearly compounding, the rate per half-year is 2.5%. We need $64000(1.025)^n = 68921$, and $(1.025)^3 \approx 1.07689$, which matches the ratio. So $n=3$ half-years = 1 year 6 months.

Question 3

The principal that yields a compound interest of ₹420 during the second year at 5% per annum is:

Accepted Answer

₹8000. The compound interest earned in the second year is interest on the amount after the first year. So second-year interest = $P \times 1.05 \times 0.05 = 0.0525P$. Given this equals 420, we get $P = 420/0.0525 = 8000$.

Question 4

₹800 at 5% per annum compounded annually will amount to ₹882 in how many years?

Accepted Answer

2 year. For annual compounding, the amount is $A=P(1+r/100)^n$. Here $882=800(1.05)^n$, so $882/800=1.1025=(1.05)^2$. Hence, $n=2$ years.

Question 5

A man saves ₹2000 at the end of each year and invests the money at 5% compound interest. At the end of 3 years, he will have:

Accepted Answer

₹6305. The deposits are made at the end of each year, so their maturity values are $2000(1.05)^2$, $2000(1.05)$, and $2000$. Adding them gives $2205+2100+2000=6305$.

Question 6

If the rate of interest is 4% per annum for the first year, 5% per annum for the second year, and 6% per annum for the third year, then the compound interest on ₹10000 for 3 years will be:

Accepted Answer

₹1575.20. With varying annual rates, the amount becomes $10000\times1.04\times1.05\times1.06=11575.20$. Subtracting the principal gives compound interest $=11575.20-10000=1575.20$.

Question 7

The compound interest on ₹8000 at 15% per annum for 2 years 4 months, when compounded annually, is:

Accepted Answer

₹3109. For annual compounding, first compound for 2 years: $8000(1.15)^2=10580$. For the remaining 4 months, take simple interest on this amount: $10580\times15\%\times\frac{4}{12}=529$. Total CI = $10580-8000+529=3109$.

Question 8

A certain amount of money earns ₹540 as simple interest in 3 years. If it earns compound interest of ₹376.20 at the same rate of interest in 2 years, find the principal amount (in ₹).

Accepted Answer

2000. From simple interest, $P\times r\times 3/100=540$, so $Pr=18000$. For 2 years, $CI-SI=\frac{Pr^2}{10000}$. Using $CI=376.20$ and $SI=\frac{Pr\times2}{100}=360$, the difference is $16.20$, which gives $P=2000$.

Question 9

There is a 100% increase in an amount in 8 years at simple interest. Find the compound interest on ₹8000 after 2 years at the same rate of interest.

Accepted Answer

₹2125. If the amount doubles in 8 years at simple interest, then SI in 8 years equals principal, so the rate is $100/8=12.5\%$ p.a. For 2 years, CI on ₹8000 is $8000[(1.125)^2-1]=8000(1.265625-1)=2125$.

Question 10

The compound interest on a certain sum of money invested for 2 years at 5% per annum is ₹328. The simple interest on the sum, at the same rate and for the same period, will be:

Accepted Answer

₹320. For 2 years at rate $r$, $CI-SI=\frac{Pr^2}{10000}$. Here $CI=328$ and $r=5\%$, so the difference is $P\times25/10000=0.0025P$. Solving gives $P=3200$, and hence $SI=\frac{3200\times5\times2}{100}=320$.

Question 11

The compound interest on a certain sum for two successive years is ₹225 and ₹238.50. The rate of interest per annum is:

Accepted Answer

6%. In compound interest, the interest earned in the second year is the first year's interest multiplied by $1+r/100$. So $238.50/225=1.06$, which gives $r=6\%$.

SSC CGL (Prelims) Maths: Compound Interest questions with solutions

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