Question

John wants to buy a new sports car, and he estimates that he'll need 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:

Answer 1

John should deposit John wants to deposit enough money to reach $2939.78 into his account.

Step-by-step explanation:

To find out how much John should deposit into his account, we can use the formula for compound interest: A = P*e^(rt), where A is the final amount, P is the principal amount, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.

In this case, John wants to deposit enough money to reach $3,075.00 after 22 months (approximately 1.83 years), and the account earns 5.694% interest compounded continuously.

Using the formula, we can set up the equation: 3075 = P * e^(0.05694 * 1.83).

Solving for P: P = 3075 / (e^(0.05694 * 1.83)). Using the value of e and rounding to two decimal places, we find that John should deposit $2939.78 into his account.