To save for a new car, Trafton invested $7,000 in a savings account that earns 5.5% interest, compounded continuously. After four years, he wants to buy a used car for $9,000. 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

Emerson Whitaker

3 March, 13:04

To save for a new car, Trafton invested $7,000 in a savings account that earns 5.5% interest, compounded continuously. After four years, he wants to buy a used car for $9,000. 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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Sarahi · Answer 1

Answer: he needs to add $277.5

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 = $7,000

r = 5.5% = 5.5/100 = 0.055

t = 4 years

Therefore,

A = 7000 x e (0.055 x 4)

A = 7000 x e (0.22)

A = $8722.5

After four years, he wants to buy a used car for $9,000. Therefore, the additional amount that he needs to add is

9000 - 8722.5 = $277.5