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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 :

Answer:

(a)[tex]A=\$13,116.51[/tex]

(b)  [tex]A=\$13,157.04[/tex]

(c) [tex]A=\$13,165.30[/tex]

Step-by-step explanation:

Formula of compound interest:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Compound continuously

[tex]A=Pe^{rt}[/tex]

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]

[tex]A=10000(1+\frac{0.055}{2})^{2\times 5}[/tex]

[tex]\Rightarrow A=10000(1+\frac{0.055}{2})^{10}[/tex]

[tex]\Rightarrow A=\$13,116.51[/tex]

(b)

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

[tex]A=10000(1+\frac{0.055}{12})^{12\times 5}[/tex]

[tex]\Rightarrow A=10000(1+\frac{0.055}{12})^{60}[/tex]

[tex]\Rightarrow A=\$13,157.04[/tex]

(C)

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

[tex]A=10,000e^{0.055 \times 5}[/tex]

[tex]\Rightarrow A=10000e^{0.275}[/tex]

[tex]\Rightarrow A=\$13,165.30[/tex]

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