Question

Tamira invests $5,000 in an account that pays 4% annual interest. How much will there be in the account after 3 years if the interest is compounded annually, semi-annually, quarterly, or monthly?

Answer 1

There will be $5624.32 in the account after 3 years if the interest is compounded annually.

There will be $5630.812 in the account after 3 years if the interest is compounded semi-annually.

There will be $5634.125 in the account after 3 years if the interest is compounded quarterly.

There will be $5636.359 in the account after 3 years if the interest is compounded monthly

Explanation:

Tamira invests $5,000 in an account

Rate of interest = 4%

Time = 3 years

Case 1:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 1

Formula :
`A=P(1+r)^t`

`A=5000(1+0.04)^3`

A=5624.32

There will be $5624.32 in the account after 3 years if the interest is compounded annually.

Case 2:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 2

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

`A=5000(1+(0.04)/(2))^(2 * 3)`

A=5630.812

There will be $5630.812 in the account after 3 years if the interest is compounded semi-annually.

Case 3:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 4

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

`A=5000(1+(0.04)/(4))^(4 * 3)`

A=5634.125

There will be $5634.125 in the account after 3 years if the interest is compounded quarterly.

Case 4:

Principal = 5000

Rate of interest = 4%

Time = 3 years

No. of compounds per year = 4

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

`A=5000(1+(0.04)/(12))^(12 * 3)`

A=5636.359

There will be $5636.359 in the account after 3 years if the interest is compounded monthly