Question

Destiny is saving up money to buy a car. Destiny puts $8,000.00 into an account which earns 11% interest, compounded quarterly. How much will she have in the account after 5 years? p{1+) Use the formula A = P 1 + where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.

Answer 1

`\text{\$13,763.45}`

Step-by-step explanation

We want to find the amount she will have after 5 years.

To do this, we apply the compound interest formula:

`A=P(1+(r)/(n))^(nt)`

From the question:

`\begin{gathered} P=\text{ \$8000} \\ r=11\text{ \%= 0.11} \\ n=4 \\ t=5 \end{gathered}`

n is 4 because there are 4 quarters in a year.

Therefore, we have that in 5 years, the amount she will have is:

`\begin{gathered} A=8000(1+(0.11)/(4))^((4\cdot5)) \\ A=8000(1+0.0275)^(20)=8000(1.0275)^(20) \\ A\approx\text{ \$13,763.45} \end{gathered}`

That is how much she will have in 5 years.