Question

Suppose you have determined that you want to have retirement savings of $5,000,000 when you retire at age 65, 42 years after you graduate, at age 23. Looking at the long history of the market, you are confident that you can earn at 10% per annum on a well-diversified equity portfolio.

a) Calculate much would you have to save annually at the end of each year for the next 42 years to reach your $5,000,000 goal assuming a 10% annual rate of return?

b) How much would you need to invest at age 23 to have $5,000,000 in your portfolio at age 65?

c) To avoid carry-forward issues, we will assume that the answer in part (a) is $100,000. Suppose that at age 23, you borrow $100,000, paying interest at 4.5% APR, compounded monthly on a 10-year amortization. What would be your monthly payments?

Answer 1

a) Savings annually at the end of each year for the next 42 years to reach your $5,000,000 goal assuming a 10% annual rate of return.

Future value = Savings * FV of an annuity factor.

Future value = 5,000,000

FV of an annuity factor = ([1 + r]^n - 1 )/r

   = (1+0.10)⁴²-1)/0.10

= 537.37

Savings = Future value/FV of an annuity factor.

=5,000,000/537.37

=$ 9304.57

b) investment at age 23 to have $5,000,000 in portfolio at age 65.

FV = PV * (1+r)ⁿ

5000000 = PV * (1+0.10)⁴²

PV = 5000000 / (1+0.10)⁴²

=$ 91302.52

c) Suppose that at age 23, you borrow $100,000, paying interest at 4.5% APR, compounded monthly on a 10-year amortization. What would be your monthly payments?

FV = Payment * ((1 + r/12)^n/12 - 1)/(r/12)

FV = Payment * ((1 + .045/12)^10*12 - 1)/(.045/12)

FV = Payment * ((1.567 - 1)/(.045/12)

Payment =FV /151.20

=661.37