Question

John Fillmore’s lifelong dream is to own his own fishing boat to use in his retirement. John has recently come into an inheritance of $421,800. He estimates that the boat he wants will cost $341,400 when he retires in 5 years. How much of his inheritance must he invest at an annual rate of 12% (compounded annually) to buy the boat at retirement?

Answer 1

John Fillmore must invest $53,739.68 of his inheritance annually to buy the boat at retirement.

Step-by-step explanation:

To determine this, we employ the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:

FV = M * (((1 + r)^n - 1) / r) ................................. (1)

Where,

FV = Future value or the amount of the boat he wants = $341,400

M = Annual investment required = ?

r = Annual interest rate = 12%, or 0.12

n = number of yeas = 6

Substituting the values into equation (1) and solve for M, we have:

$341,400 = M * (((1 + 0.12)^5 - 1) / 0.12)

$341,400 = M * 6.35284736

M = $341,400 / 6.35284736

M = $53,739.6824846741

Approximating to 2 decimal places, we have:

M = $53,739.68

Therefore, John Fillmore must invest $53,739.68 of his inheritance annually to buy the boat at retirement.