Question

Dee invested $3000 in a savings account that earns 6.5% interest, compounded continuously. After 4 years, he wants to buy a used car for $4000. How much money will he need to pay in addition to what is in his savings account?

Answer 1

We can use the formula for continuous compounding to find the balance in Dee's savings account after 4 years:

A = Pe^(rt)

where A is the balance, P is the principal (initial investment), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

Plugging in the values given, we get:

A = 3000*e^(0.065*4)
A = 3000*e^0.26
A = 3000*1.297
A = 3891.60

So Dee's savings account will have a balance of $3891.60 after 4 years.

To buy the used car for $4000, Dee will need to pay an additional:

4000 - 3891.60 = $108.40

Therefore, Dee will need to pay an additional $108.40 in addition to what is in his savings account to buy the used car.