Question

the compound interest of a sum of money for 1 year and 2 years are rs 450 and rs 945 respectively. find the rate of interest compounded yearly and he sum.

Answer 1

The answer is below

Explanation:

The compound interest is given by the formula:

`A=P(1+(r)/(n) )^(nt)`

Where A is the final amount, p is the principal (initial amount), r is the rate, t is the number of period and n is the number of times it was compounded per period.

Given that:

The interest is compounded yearly, i.e n = 1, for 1 year, t = 1, the compound interest is Rs 450 i.e A = 450. Therefore:

`450=P(1+(r)/(1) )^(1*1)=P(1+r)\\450=P(1+r).\ .\ .\ (1)`

For 2 year, t = 2, the compound interest is Rs 945 i.e A = 945. Therefore:

`945=P(1+(r)/(1) )^(1*2)=P(1+r)^2\\945=P(1+r)^2.\ .\ .\ (2)`

Dividing equation 2 by equation 1 gives:

2.1 = 1 + r

r = 2.1 - 1 = 1.1

r = 1.1

Put r = 1.1 in 450 = P(1 + r)

450 = P(1 + 1.1)

450 = 1.11P

P = 405.4

Therefore the rate is 1.1 = 110% and P = Rs 405.4