Question

Kelsey deposited 800.00 in a savings account earning 14% interest, compounded annually. To the nearest cent, how much interest will she earn in 5 years?

Answer 1

The accrued amount of an investment is equal to the sum of the principal amount and the interest earned:

$A=P+I$

Write the expression in terms of the interest:

$I=A-P$

To calculate the interest, the first step is to determine the accrued amount after 5 years.

The savings account compounds annually, to determine the accrued amount you have to apply the following formula:

$A=P(1-\frac{r}{n})^{nt}$

Where

A is the accrued amount

P is the principal amount

r is the interest rate expressed as a decimal value

t is the time in years

n is the number of compounding periods

The principal amount is P= $800

The interest rate of the account is 14%, to express it as a decimal value, divide it by 100

$\begin{gathered} r=\frac{14}{100} \\ r=0.14 \end{gathered}$

The time period for the investment is 5 years.

The account compounds annually, which means that there is only one compounding period per year, so, n=1.

Calculate the accrued amount:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=800(1+\frac{0.14}{1})^{1\cdot5} \\ A=800(1+0.14)^5 \\ A=800(1.14)^5 \\ A=1540.33 \end{gathered}$

After 5 years the accrued amount will be A= $1540.33

Finally, calculate the interest:

$\begin{gathered} I=A-P \\ I=1540.33-800 \\ I=740.33 \end{gathered}$

After 5 years she will have $740.33 of interest.