Question

Use the compound interest formulas Aand A = Pert to solve. Find the accumulatedvalue of an investment of $5000 at 10% compounded quarterly for 5 years.

Answer 1

Step 1. The information that we have is:

The principal amount of the investment:

$P=5,000$

The interest rate:

$r=10\text{ percent}$

we will need the interest rate as a decimal number so we divide it by 100:

$\begin{gathered} r=10/100 \\ r=0.1 \end{gathered}$

We also know that the amount is compounded quarterly, which means that it is compounded 4 times per year, this will be the value of n:

$n=4$

Finally, we have the time in years:

$t=5$

Step 2. The two formulas given are:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=Pe^{rt} \end{gathered}$

In these formulas A is the final amount of the investment after time t. The first formula is for compounding n times per year, and the second formula is for continuous compounding.

In this case, we need to use the first formula.

Step 3. Substituting the known values from step 1 into the formula:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=5000(1+\frac{0.1}{4})^{4\times5} \end{gathered}$

Step 4. Solving the operations:

$\begin{gathered} A=5,000(1+0.025)^{20} \\ \downarrow \\ A=5,000(1.025)^{20} \\ \downarrow \\ A=5,000(1.63861644) \\ \downarrow \\ A=\boxed{8,193.08} \end{gathered}$

The accumulated value of the investment is $8,193.08

Answer:

$8,193.08