Question

You are saving for your child's college education. You plan on making a total of six tuition payments each one-year apart (college plus a masters program). The annual estimated tuition payment will be made 14-years from today (at t=14), and you estimate that payment will be $50,000. The remaining five-payments will be made from t=15 to t=19. You decide to make 15 yearly contributions into an investment account. The first contribution is made today (t=0) and your last contribution will be at t=14 (the same time you make your first tuition payment), you expect your investment account will earn 8% per year. Under this plan how much will you contribute annually? i. (15 pts) Write down the discounted cash flow equation. ii. (10 pts) Solve the equation to find the annual contribution amount.

Answer 1

annual contribution = $8,512.93

Step-by-step explanation:

total payments = $50,000 x 6 (years 14 to 19)

you will make 15 yearly contributions, one today and 14 annual contributions until year 14.

We must first determine the present value of the distributions (the money that you will require to pay for college). You will take 6 distributions of $50,000, starting on year 14:

present value of annuity due = annual distribution + {annual distribution x [1 - (1 + r)⁻⁽ⁿ⁻¹⁾]/r}

present value of annuity due = $50,000 + {$50,000 x [1 - (1 + 0.08)⁻⁵]/0.08} = $50,000 + $199,635.50 = $249,635.50

This means that the future value of your contributions (by year 14) must be $249,635.50. In order to determine the amount of your contributions, we must use the future value of an annuity due formula:

future value = (1 + r) x contribution x {[(1 + r)ⁿ - 1]/r}

since we know the future value, then we will use the following formula:

contribution = future value / [(1 + r) x {[(1 + r)ⁿ - 1]/r}]

contribution = $249,635.50 / [(1 + 0.08) x {[(1 + 0.08)¹⁵ - 1]/0.08}] = $249,635.50 / 29.32428304 = $8,512.93