Question

A sum of money invested at the compound interest payable yearly has interest in

2 years and 4 years are Rs. 4,200 and Rs. 9282 respectively. Find the rate of
interest​

Answer 1

49% and 30% respectively

Explanation:

Step one:

Given data

Principal = Rs. 4,200

Final Amount= Rs. 9282 respectively

time = 2 years and

time = 4 years

Required

The rate of interest for 2 and 4 years

Step two:

the compound interest formula is

A= P(1+r)^t

for 2 years

Substitute

`9282= 4200(1+r)^2\\\\9282/4200= (1+r)^2`

`1+r= \sqrt{(9282)/( 4200) }\\\\1+r= √(2.21) \\\\1+r= 1.49\\\\r=1.49-1\\\\r= 0.49\\\\`

the rate is 49%

For 4 years we have

`9282= 4200(1+r)^4\\\\9282/4200= (1+r)^4`

`1+r= \sqrt[4]{(9282)/(4500) } \\\\1+r=\sqrt[4]{2.21} \\\\1+r= 1.30\\\\r=1.30-1\\\\r= 0.30\\\\`

the rate is 30%