Question

To save for a new car, Trafton invested $3,000 in a savings account that earns 1.5% interest, compounded continuously. After four years, he wants to buy a used car for $4,000. How much money will he need to pay in addition to what is in his savings account? (Round your answer to the nearest cent.)

Answer 1

ANSWER:

$814.49

STEP-BY-STEP EXPLANATION:

Given:

Principal (P) = $3000

Rate (r) = 1.5%

Tim (t) = 4

For continuously compounded formula is the following:

$\begin{gathered} A=P\cdot e^{rt} \\ \\ \text{ We replacing:} \\ \\ A=3000\cdot e^{0.015\cdot4} \\ \\ A=3185.51 \end{gathered}$

This means after 4 years Trafton has $3185.51 in his savings account, what he needs to get up to $4000 is calculated by the following subtraction:

$\begin{gathered} a=4000-3185.51 \\ \\ a=841.49 \end{gathered}$

This means that he needs an additional $814.49 to buy the car.