Question

7. In how many years will a sum of Rs 5,120 amount to Rs 7,290 at the compound interest rate of
8. In how many full years will a sum of money become more than double at the compound interest
9. A certain sum of money amounts to Rs 2,646 in 2 years and to Rs 2,778.30 in 3 years at the same
annual compound interest rate. Find the rate of interest and the sum.​

Answer 1

Answer:

7: 3 years

7: 3 years8: 4 years

9: sum is Rs 2400 and rate of interest is 5% p.a.

Step-by-step explanation:

7 -> 7290 in 3 years at compound interest.

8 -> Thus in 4 years the sum of money becomes more than double.

9-> Given

(i) A certain sum of money amounts to Rs 2646 in 2 years

(ii) It then amounts to Rs 2778.30 in 3

years

To find:

(1) Rate of interest and sum.

Solution:

The amount (A) in compound interest is

given as: A = P(1+ r/n)^(nt)

Since interest is compounded annually,

n=1.

For first case, A = Rs 2646, t 2. = 2646 = P(1 + r)^2 ...(1)

For second case,

A= Rs 2778.30, t = 3.

2778.30 = P(1 + r)^3 ...(2)

=

Dividing (2) by (1), we get,

(2778.30/2646) = (1+r)

=> 1 + r = 21/20

=>r = 1/20

=>r = (100/20)% = 5%

So, rate = 5% p.a.

P(1 + 1/20)^2 = 2646

=> 441P/400 = 2646

=> P = Rs 2400

So, sum is Rs 2400 and rate of interest is 5% p.a.