Question

You decide you want to put away money for your older child to attend college when they graduate high school. How much money will you need to invest now if the account you are investing in gives 3.75% interest, compounded monthly, for 8 years, if you also decide to make a $100 deposit once a month, if you want the end balance to be $50,000?

Answer 1

To have an end balance of $50,000 8 years from now with a 3.75% interest rate compounded monthly and monthly deposits of $100, you will need to invest approximately $36,215.17 now.

Step-by-step explanation:

To calculate the amount of money you need to invest now, we'll use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the end balance, P is the initial investment, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

We know the end balance is $50,000, the interest rate is 3.75% (or 0.0375), the compounding is done monthly

(so n = 12), and the investment period is 8 years. We need to solve for P.

Plugging in the values:

$50,000 = P(1 + 0.0375/12)^(12*8)

Simplifying the expression:

$50,000 = P(1.003125)^(96)

Divide both sides by (1.003125)^(96):

P = $50,000 / (1.003125)^(96)

Using a calculator, we get:

P ≈ $36,215.17