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

• Annually-$5624.32
• Semi-Annually-$5630.81
• Quarterly-$5634.13
• Monthly-$5636.36

Explanation:

For an initial amount P invested at compound interest for a number of years, n compounded at a rate r% periodically with period, k:

Amount
`=P(1+(r)/(k))^(nk)`

For the given problem:

P=$5,000; r=4%-=0.04, n=3 years

Annually

k=1

Amount

`=5000(1+(0.04)/(1))^(3*1)\\=5000(1.04)^3\\=\$5624.32`

Semi-Annually

k=2

Amount

`=5000(1+(0.04)/(2))^(3*2)\\=5000(1.02)^(6)\\=\$5630.81`

Quarterly

k=4

Amount

`=5000(1+(0.04)/(4))^(3*4)\\=5000(1.01)^(12)\\=\$5634.13`

Monthly

k=12

Amount

`=5000(1+(0.04)/(12))^(3*12)\\=5000(1+(0.04)/(12))^(36)\\=\$5636.36`