Question

Rs. 100 will become ……. after 20 years at 5% p.a. compound interest amount.
A. Rs. 250
B. Rs. 205
C. Rs. 265.5
D. none of the above

Answer 1

Hint: We first try to find out the general formula of compound interest with the principal. We use the given values of rate and time in the formula to find the outcome of the 100 Rs. after 20 years. The given rate is based on per annum and that’s why we don’t need to use the division of the interest rate.

Complete step-by-step solution:
The amount of 100 Rs. has been invested for 20 years at 5% p.a. compound interest amount.
The general formula of compound interest added with principal for principal amount p with r% for n years will be A then $A=p{{\left( 1+\dfrac{r}{100} \right)}^{n}}$.
In our given problem the respective values of the variables are $p=100,r=5,n=20$.
Putting all the values we get the compound interest added with principal value as
$A=100{{\left( 1+\dfrac{5}{100} \right)}^{20}}=100{{\left( 1.05 \right)}^{20}}=265.33\approx 265.5$
The correct option is C.

Note: There is no direct formula to find the interest-only in case of compound interest. We have to find the total and then subtract the principal to find the interest. If in any case we use the rate of interest as half-yearly or quarterly based in that case the formula changes to \[A=p{{\left( 1+\dfrac{r}{100\times 2} \right)}^{n}}\] and $A=p{{\left( 1+\dfrac{r}{100\times 4} \right)}^{n}}$ respectively. The iteration of the interest comes into play within a year.