Question

Suppose someone wants to accumulate ​$65,000 for a college fund over the next 15 years. Determine whether the following investment plans will allow the person to reach the goal. Assume the compounding and payment periods are the same. The person deposits ​$ 130per month into an account with an APR of ​7%.

Answer 1

The investment plan of depositing $130 per month into an account with an APR of 7% will not allow the person to accumulate $65,000 in 15 years.

Step-by-step explanation:

To determine whether the given investment plan will allow the person to reach the goal of accumulating $65,000 in 15 years, we need to calculate the future value of the monthly deposits using compound interest formula.

1. Convert the APR into a decimal by dividing it by 100: 7% = 0.07.
2. Calculate the monthly interest rate by dividing the annual interest rate by 12: 0.07 / 12 = 0.00583.
3. Calculate the number of months in 15 years: 15 * 12 = 180 months.
4. Use the future value formula: FV = P * (1 + r)^n, where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of months.
5. Substitute the given values into the formula: FV = 130 * (1 + 0.00583)^180.
6. Calculate the future value: FV ≈ $47,266.30.
7. Since the future value is less than the desired goal of $65,000, the investment plan will not allow the person to reach the goal.