Question

How much money will you have in 5 years if you invest $9000 at a 5.4% annual rate of interest compounded quarterly? How much will you have if it is compounded monthly?

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Answer 1

Answer: Amount in 5 years( if compounded quarterly) = $11,768.40

Amount in 5 years( if compounded monthly = $11782.54

Explanation:

Formula for accumulated amount in t years at annual rate of r% compounded quarterly:
`A=P(1+(r)/(4))^(4t)`

Formula for accumulated amount in t years at annual rate of r% compounded monthly:
`A=P(1+(r)/(12))^(12t)`, where P= principal amount.

Given: P= $9000, r= 5.4%= 0.054, t= 5 years

Amount in 5 years if compounded quarterly =
`9000(1+(0.054)/(4))^(4*5)`

`=9000(1.0135)^(20)\\\\=9000(1.30760044763)\approx11768.40`

i.e. Amount in 5 years( if compounded quarterly) = $11,768.40

Amount in 5 years if compounded monthly =
`9000(1+(0.054)/(12))^(12*5)`

`=9000(1.0045)^(60)\\\\=9000(1.309171267)\approx11782.54`

i.e. Amount in 5 years( if compounded monthly = $11782.54