Question

Your goal is to create a college fund for your child. Suppose you find a fund that the fees an APR of 4% . How much should you deposit monthly to accumulate $80,000 in 17 years?

Answer 1

We can use the formula for the future value of an annuity, which is:

FV = Pmt x (((1 + r)^n - 1) / r)

where:

FV is the future value we want to accumulate (which is $80,000 in this case)
Pmt is the monthly payment we need to make
r is the monthly interest rate, which we can calculate as APR / 12 (since APR is the annual interest rate)
n is the total number of payments we will make, which is the number of years times 12 (since there are 12 months in a year)

Substituting the given values, we get:

FV = Pmt x (((1 + 0.04/12)^(17*12) - 1) / (0.04/12))
$80,000 = Pmt x (((1 + 0.04/12)^(17*12) - 1) / (0.04/12))

Now we solve for Pmt:

Pmt = $80,000 / (((1 + 0.04/12)^(17*12) - 1) / (0.04/12))
Pmt = $80,000 / 216.4147
Pmt = $369.72 (rounded to the nearest cent)

Therefore, to accumulate $80,000 in 17 years with an APR of 4%, you need to deposit $369.72 per month.