Question

A sum of money becomes rs 17640 in two years and rs 18522 in three years at the same rate of interest compounded annually .Find the sum and rate of interest p.A.

Answer 1

Compound Interest Problem

Given data:

• A sum of money becomes Rs. 17640 in two years
• and Rs. 18522 in three years.

To find:

• The sum of money
• and the rate of compound interest.

Step-by-step explanation:

Let the sum be $P$ and the rate of compound interest per annum be $r\%$.

Case 1. Sum of money becomes Rs. 17640 in two years

Here,

• sum = P,
• amount, A = Rs. 17640,
• rate of interest = r% p.a.
• and time, t = 2 years

Then, $A = P (1 + \frac{r}{100})^t$

i.e., $17640 = P (1 + \frac{r}{100})^2$ .....(1)

Case 2. Sum of money becomes Rs. 18522 in three years

Here,

• sum = P,
• amount, A = Rs. 18522,
• rate of interest = r% p.a.
• and time, t = 3 years

Then, $A = P (1 + \frac{r}{100})^t$

i.e., $18522 = P (1 + \frac{r}{100})^3$ .....(2)

Now, dividing (2) by (1), we get

$\quad \frac{18522}{17640} = 1 + \frac{r}{100}$

or, $\frac{r}{100} = \frac{18522}{17640} - 1$

or, $\frac{r}{100} = \frac{18522 - 17650}{17640}$

or, $\frac{r}{100} = \frac{882}{17640}$

or, $\frac{r}{100} = \frac{1}{20}$

or, $r = 100 * \frac{1}{20}$

or, r = 5

Thus rate of compound interest is 5.17 p.a.

Putting r = 5 in (1), we get

$\quad 17640 = P (1 + \frac{5}{100})^2$

or, $P = \frac{17640}{(1 + \frac{5}{100})^2}$

or, P = 16000

Thus the sum of money is Rs. 16000