Question

1. Education Planning: Suppose you have just had your first child and you want to begin saving for their college education. You estimate that with inflation, the cost of four years of college at a top university will cost a total of $225,000 in 18 years when your child graduates from high school. How much do you need to invest at the end of each month (part a) or year (part b) for the next 18 years to accumulate the $225,000 assuming:

1. a 6% annual interest rate compounded monthly?

2. an 8% annual interest rate compounded annually?

Answer 1

Future Value to accumulate in 18 years = $225,000

a). Calculating the Periodic monthly investment if 6% annual interest rate compounded monthly using FV of annuity formula:-

Where, C= Periodic Monthly Investment

r = Periodic Interest rate = 6%/12 = 0.5%

n= no of periods = 18 years*12 = 216

C = $580.87

So, the amount you need to invest at the end of each month is $580.87

b). Interest rate is 8% annual interest rate compounded annually

Since, investmet period is monthly we will calculate Nominal Interest rate compounded monthly.

r = Nominal Interest rate compounded monthly

m = no of times compounding in a year = 12

EAR = 8%

Taking 12-root on both sides,

1.00643403011 = (1+r/12)

r = 7.7208%

Now,

Calculating the Periodic monthly investment if 7.7208% annual interest rate compounded monthly using PV of annuity formula:-

Where, C= Periodic Monthly Investment

r = Periodic Interest rate =7.7208%/12 = 0.6434

n= no of periods = 18 years*12 = 216

C = $483.20

So, the amount you need to invest at the end of each month is $1930.85

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