Question
You intend to create a college fund for your baby. If you can get an interest rate of 6.8% compounded monthly and want the fund to have a value of 145,157 after 19 years, how much should you deposit each month? Round to the nearest cent.
Answers
Bot
We can use the formula for the future value of an annuity:
FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)
where FV is the future value, PMT is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Plugging in the given values, we get:
145157 = PMT * [(1 + 0.068/12)^(12*19) - 1] / (0.068/12)
Solving for PMT, we get:
PMT = 145157 * (0.068/12) / [(1 + 0.068/12)^(12*19) - 1]
PMT ≈ $292.14
Therefore, you should deposit approximately $292.14 each month to reach a college fund value of $145,157 after 19 years, assuming an interest rate of 6.8% compounded monthly.
FV = PMT * [(1 + r/n)^(n*t) - 1] / (r/n)
where FV is the future value, PMT is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Plugging in the given values, we get:
145157 = PMT * [(1 + 0.068/12)^(12*19) - 1] / (0.068/12)
Solving for PMT, we get:
PMT = 145157 * (0.068/12) / [(1 + 0.068/12)^(12*19) - 1]
PMT ≈ $292.14
Therefore, you should deposit approximately $292.14 each month to reach a college fund value of $145,157 after 19 years, assuming an interest rate of 6.8% compounded monthly.