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

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

$A=10,000e^{0.055 \times 5}$

$\Rightarrow A=10000e^{0.275}$

$\Rightarrow A=\ 13,165.30$