Question

Use the compound interest formulas Upper A equals Upper P (1 plus StartFraction n Over n EndFraction )Superscript nt and Upper A equals Pe Superscript rt to solve the problem given. Round answers to the nearest cent. Find the accumulated value of an investment of $ 10 comma 000 for 5 years at an interest rate of 5.5 % if the money is a. compounded​ semiannually; b. compounded​ quarterly; c. compounded monthly d. compounded continuously.

Answer 1

(a)
`A=\$13,116.51`

(b)
`A=\$13,157.04`

(c)
`A=\$13,165.30`

Explanation:

Formula of compound interest:

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

Compound continuously

`A=Pe^(rt)`

A= Amount after t years

P= Principal

r= rate of interest

a)

P=10,000, r=5.5%= 0.055 and t= 5 years, n=2 [ compounded semiannually]

`A=10000(1+(0.055)/(2))^(2* 5)`

`\Rightarrow A=10000(1+(0.055)/(2))^(10)`

`\Rightarrow A=\$13,116.51`

(b)

P=10,000, r=5.5%= 0.055 and t= 5 years, n=12 [ compounded monthly]

`A=10000(1+(0.055)/(12))^(12* 5)`

`\Rightarrow A=10000(1+(0.055)/(12))^(60)`

`\Rightarrow A=\$13,157.04`

(C)

P=10,000, r=5.5%= 0.055 and t= 5 years

`A=10,000e^(0.055 * 5)`

`\Rightarrow A=10000e^(0.275)`

`\Rightarrow A=\$13,165.30`