Question

ohn wants to buy a new sports car, and he estimates that he'll leed to make a $3,075.00 down payment towards his purchase. If he has 22 months to save up for the new car, how much should he deposit into his account if the account earns 5.694% compounded continuously so that he may reach his goal? John needs to deposit (Note: Your answer should have a dollar sign and be accurate to two decimal places) Answer(s) submitted: (incorrect)

Answer 1

John needs to use the continuous compound interest formula to determine how much to deposit to reach his $3,075 goal in 22 months at an interest rate of 5.694%, compounded continuously.

Step-by-step explanation:

John wants to calculate how much he needs to deposit into an account that earns 5.694% interest compounded continuously to reach his goal of a $3,075.00 down payment in 22 months. To do this, the formula for continuous compound interest is P = A / e(rt), where P is the principal (the amount needed to deposit), A is the amount desired in the future, r is the annual interest rate (as a decimal), and t is the time in years.

In this case, John's A is $3,075, r is 0.05694, and t is 22/12 years (since there are 12 months in a year). So his equation would be:

P = 3075 / e(0.05694 × (22/12))

After calculating the value of the right side of the equation, John will know the amount he needs to deposit today to have $3,075.00 in 22 months with the given interest rate.