Question

A sum of money becomes Rs. 13,380 after 3 years and Rs. 20,070 after 6 years on compound interest. The sum (in rupees) is:
a. 8800
b. 8890
c. 8920
d. 9040

Answer 1

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Option c. 8920 is correct


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Answer 2

Option (c) is correct

Concept:

Compound interest formula:

Compound interest for n years

$=P(1+\frac{r}{100})^n-P$

Amount acquired after n years

=$=P(1+\frac{r}{100})^n$

As per given data,

When n=3, Amount = Rs.13380

$Amount=P(1+\frac{r}{100})^n\\\\13380=P(1+\frac{r}{100})^3$.............(1)

When n=6, Amount = Rs.20070

$Amount=P(1+\frac{r}{100})^n\\\\20070=P(1+\frac{r}{100})^6$.............(2)

Squaring (1) we get

$(13380)^2=P^2(1+\frac{r}{100})^6\\\\(13380)(13380)=P[P(1+\frac{r}{100})^6]\\\\(13380)(13380)=P[20070]\\\\P=\frac{(13380)(1338)}{2007}\\\\P=\frac{13380(2)}{3} (reduced \:by \:669)$

P=4460×2

P= Rs.8920