Question

Savings with periodic rates. What investment does Patrick need to make at the end of each month into his savings account over the coming 31 months to reach his vacation goal of $8,000 if he is getting 10% APR on his account? What investment does Patrick need to make at the end of each month into his savings account? $ (Round to the nearest cent.)

Answer 1

To achieve his $8,000 vacation goal in 31 months with a 10% APR account, Patrick needs to calculate the monthly investment using the future value of an annuity formula. By rearranging the formula to solve for P (periodic payment), he can determine the exact amount needed each month.

Step-by-step explanation:

Patrick needs to calculate the periodic investment required to reach his $8,000 vacation goal with a 10% APR savings account, compounded monthly over 31 months. To find this, we can use the future value of an annuity formula which considers the periodic rate and the number of periods.The formula for the future value of an annuity (FVA) is FVA = P * [((1 + r)^n - 1) / r], where P is the periodic payment, r is the monthly interest rate, and n is the number of periods.

Given that the annual interest rate is 10%, we first have to find the monthly interest rate which is 0.10/12, and the number of periods is 31 months. We rearrange the FVA formula to solve for the periodic payment P, and we aim for a future value (FVA) of $8,000.