To save for a new car, Trafton invested $3,000 in a savings account that earns 4.5% 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.)

Question

Mathematics

Aliyah Chen

9 March, 09:49

To save for a new car, Trafton invested $3,000 in a savings account that earns 4.5% 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.)

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Answers (1)

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Kolton Macias · Answer 1

Answer: he needs an additional $408.3 to buy the car.

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

From the information given,

P = $3000

r = 4.5% = 4.5/100 = 0.045

t = 4 years

Therefore,

A = 3000 x e^ (0.045 x 4)

A = 3000 x e^ (0.18)

A = $3591.7

He wants to buy a used car for $4,000. The additional amount that he needs is

4000 - 3591.7 = $408.3