Question

Use the compound interest formulas A=P and A=Per to solve the problem given. Round answers to the nearest cent. Find the accumulated value of an investment of $20,000 for 4 years at an interest rate of 6% if the money is a. compounded semiannually, compounded monthly, d. compounded continuously a. What is the accumulated value if the money is compounded semiannually? $ (Round your answer to the nearest cent. Do not include the $ symbol in your answer.) b. What is the accumulated value if the money is compounded quarterly?

Answer 1

Answer:

$\begin{gathered} a)\text{ }A=25,335.40 \\ b)\text{ }A=25,409.78 \\ c)\text{ }A=25,424.48 \\ d)\text{ }A=25,379.71 \end{gathered}$

Step-by-step explanation:

Compound interest is represented by the following expression:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ A=\text{ amount} \\ P=\text{ Principal} \\ r=\text{ Interest rate decimal form} \\ n=\text{ number of times interest is compounded per unit t} \\ t=\text{time} \end{gathered}$

Then,

a) Compounded semiannually:

If semi-annually, then n=2.

$\begin{gathered} A=20,000(1+\frac{0.06}{2})^{2\cdot4} \\ A=20,000(1.03)^8 \\ A=25,335.40 \end{gathered}$

b) Compounded monthly:

If monthly, then n=12

$\begin{gathered} A=20,000(1+\frac{0.06}{12})^{12\cdot4} \\ A=20,000(1.005)^{48} \\ A=25,409.78 \end{gathered}$

c) Compounded continuously:

If continuously (daily), then n=365

$\begin{gathered} A=20,000(1+\frac{0.06}{365})^{365\cdot4} \\ A=25,424.48 \end{gathered}$

d) Compounded quarterly:

If quarterly, then n=4.

$\begin{gathered} A=20,000(1+\frac{0.06}{4})^{4\cdot4} \\ A=25,379.71 \end{gathered}$