# Compound Interest and Rate Essay

1830 Words Oct 13th, 2010 8 Pages
Solution to Problem Set 1

1. You are considering various retirement plans. Your goal is to have a lump sum of \$3,000,000 available (‘in the bank’) when you retire at age 67. The various plans, with their payment schedules, are listed below. In each case, calculate the payment(s) that must be made into the plan to ensure that you have the \$3,000,000 available. For each plan, you may assume that your opportunity cost of funds is 6% per year; for each plan, you may assume that the phrase “at age XX” means the same thing as “on your XX’th birthday”.

Plan 1: Single lump sum at age 25

Plan 2: Single lump sum at age 50

Plan 3: Equal annual payments, commencing at age 31 and ending at age 67

Plan 4: Equal annual
Assume the education inflation rate of 6.4% per year, compounded monthly.

With a target of \$430,182.98, we must have:

V0 = 430,182.98/(1.061678)16

V0 = \$165,108.48

h) Calculate the monthly payment you must make into your child’s college account to pay for four years of college under the assumption that tuition will grow at the general inflation rate; you may assume that the first payment into the college account comes in one month’s time and the last payment will come one month prior to the first college tuition payment.

At the general inflation rate, our target at t=16, or (16X12 = 192 months from now) is \$214,339.59. Note that the payments are an annuity, starting in month 1 and ending in month (16*12) – 1, or month 191. Consequently, the annuity lasts for 191 months.

If we use our standard annuity compound factor formula, we’ll calculate a value at the end of the 191st month. We need to adjust our target value by one month.

V (month 191) = 214,339.59/(1+m), where m is the monthly rate that they’ll earn in the account.

The effective monthly opportunity cost of funds is 0.5%.

C * Annuity compound factor (0.50%, 191) = 214,339.59/(1.0050)

C * 318.50 = 213,273.22

C = \$669.62

i) Calculate the monthly payment you must make into your child’s college account to pay for four years of college under the assumption that tuition

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