Question

A man deposits $ 14,850 into a bank, which pays 4% interest that is compounded

semiannually. What will he have in his account at the end of three years?​

Answer 1

Given:

Principal = $14850

Rate of interest = 4% compounded semiannually.

Time = 3 years

To find:

The amount after 3 years.

Solution:

Formula for amount is:

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

Where, P is principal, r is the rate of interest in decimal, n is the number of times interest compounded and t is the number of years.

The interest is compounded semiannually, so n=2.

Putting
`P=14850, r=4, n=2, t=3` in the above formula, we get

`A=14850\left(1+(0.04)/(2)\right)^(2(3))`

`A=14850\left(1+0.02\right)^(6)`

`A=14850\left(1.02\right)^(6)`

On further simplification, we get

`A=14850(1.12616242)`

`A=16723.511937`

`A\approx 16723.51`

Therefore, the amount in the account after three years is $16723.51.