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

Mario Cooke

Mathematics

16 June, 23:48

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.)

+1

Answers (1)

Know the Answer?

Cisco · 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