Question

A sum of money becomes 17640 in two
years and 18522 in 3 years at the same rate
of interest, compounded annually. Find the
sum and the rate of interest per annum.​

Answer 1

Answer:

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 PP and the rate of compound interest per annum be r\%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})^tA=P(1+

100

r

)

t

i.e., 17640 = P (1 + \frac{r}{100})^217640=P(1+

100

r

)

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})^tA=P(1+

100

r

)

t

i.e., 18522 = P (1 + \frac{r}{100})^318522=P(1+

100

r

)

3

.....(2)

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

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

17640

18522

=1+

100

r

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

100

r

=

17640

18522

−1

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

100

r

=

17640

18522−17650

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

100

r

=

17640

882

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

100

r

=

20

1

or, r = 100 * \frac{1}{20}r=100∗

20

1

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})^217640=P(1+

100

5

)

2

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

(1+

100

5

)

2

17640

or, P = 16000

Thus the sum of money is Rs. 16000