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+(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+(r)/(n))^(nt) \\ A=5000(1+(0.1)/(4))^(4*5) \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