Question : Jonathan had borrowed a sum of money 3 years ago at 10% interest per annum compounded annually for 5 years, with the amount to be paid at the end of the period being INR 1,61,051. However, there is no pre-payment penalty and Jonathan has received some bonus payments now, with which he has decided to clear his debt. How much does Jonathan have to pay now to clear his debt?
Option 1: INR 1,33,000
Option 2: INR 1,32,900
Option 3: INR 1,33,142
Option 4: INR 1,33,200
Correct Answer: INR 1,33,142
Solution :
Amount = P (1 + $\frac{r}{n})^{nt}$, where
P = Principal
r = rate of interest (in decimal)
n = number of times
t = time in years
According to the question
⇒ P = $\frac{A}{(1+\frac{r}{n})^{nt}}$
= $\frac{161051}{(1+\frac{0.1}{1})^{5}}$
= $\frac{161051}{(1+\frac{0.1}{1})^{5}}$
= $\frac{ 161051}{1.61}$
= 100031.68
He borrowed INR 100031.68 for 3 years
So amount to be paid (A) = P${(1+\frac{r}{n})^{nt}}$ = 100031.68(1 + $\frac{0.1}{1})^{3}$
= 100031.68 × 1.331
= 1,33,142
Hence, the correct answer is INR 1,33,142.
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