Question

Suppose you currently have no wealth or income, but will receive a $1,000,000 inheritance 15 years from today. You would like to borrow against this future windfall such that you spend equal annual amounts of $X each year, starting today (at t=0) and ending in 15 years (at t=15). If your bank charges you 5 percent annually to borrow money, what is the maximum amount, $X, that you can spend at each point in time?

Answer 1

So, there are in all 16 payments that should be equal to $1,000,000. one payment today and 15 ordinary annuity payments. Future value of all these 16 payments will be equal to $1,000,000 at 5% rate.

FV of an ordinary annuity is mathematically represented as:

For a lumpsum amount, FV = PV * (1 + r)ⁿ.

We will divide our 16 payments into 2 - one lumpsum payment today and 15 ordinary annuity payments

1,000,000 = 2.0789P + 21.5786P

1,000,000 = 23.6575P

P = $42,269.91 --> Maximum amount that could be spent