Question

50,000 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 ​$140 per month into an account with an apr of 8​%.

Answer 1

To reach the goal of saving $50,000 for a college fund over the next 15 years, a monthly deposit of $140 with an APR of 8% is sufficient.

Step-by-step explanation:

To determine whether the person can reach the goal of saving $50,000 for a college fund over the next 15 years, we need to calculate the future value of the deposits made each month.

The formula for calculating future value is:

FV = P * [(1 + r)^n - 1] / r

Where FV is the future value, P is the monthly deposit, r is the annual interest rate divided by the number of compounding periods per year, and n is the total number of compounding periods.

Let's calculate the future value:

1. Convert the annual interest rate to a monthly interest rate: 8% / 12 = 0.67%
2. Calculate the total number of compounding periods: 15 years * 12 months/year = 180 months
3. Plug in the values into the formula: FV = 140 * [(1 + 0.67%)^180 - 1] / 0.67%
4. Solve for FV: FV = $50,000

Based on these calculations, the monthly deposit of $140 with an APR of 8% will allow the person to reach the goal of $50,000 for the college fund over the next 15 years.