A sum of money amounts to ₹ 28224 in 2 {yr} and to ₹ 29635.20 in 3 {yr} when invested on compound interest, compounded annually. What is the sum of money?

SSC CHSL 13 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 58 of 100

Marks: +1, -0

A sum of money amounts to

₹ 28224

2 {yr}

and to

₹ 29635.20

3 {yr}

when invested on compound interest, compounded annually.
What is the sum of money?

Solution:

Let the principal be

₹ P

and rate of interest be

r \%

.
We know that

A=P[1+\;{r}/{100}]^{t}

According to the question,

28224 \;\; =P(1+\;{r}/{100})^{2}

. . . (i)

\;\text " and "\; 29635.20 \;\; =P(1+\;{r}/{100})^{3}

. . . (ii)

\;\text " Divide Eq. (ii) by Eq. (i); "\;

⇒ \;\; 1+\;{r}/{100} \;\; =\;{29635.20}/{28224}

⇒ \;\; \;{r}/{100} \;\; =\;{2963520}/{28224}-1

⇒ \;\; \;{r}/{100} \;\; =\;{2963520-28224}/{28224}

\;{r}/{100} \;\; =\;{14112}/{28244}

⇒ \;\; r=5 \%

Put the value of

r

in Eq. (i),

P \;\; =28224 × \;{20}/{21} × \;{20}/{21}

\;\; =₹ 25600 .

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