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kumpel [21]
4 years ago
5

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.
Mathematics
1 answer:
MatroZZZ [7]4 years ago
6 0

Answer:

(a)A=\$13,116.51

(b)  A=\$13,157.04

(c) A=\$13,165.30

Step-by-step explanation:

Formula of compound interest:

A=P(1+\frac{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+\frac{0.055}{2})^{2\times 5}

\Rightarrow A=10000(1+\frac{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+\frac{0.055}{12})^{12\times 5}

\Rightarrow A=10000(1+\frac{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 \times 5}

\Rightarrow A=10000e^{0.275}

\Rightarrow A=\$13,165.30

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