Question

After 25 years, what is the difference between a couple going into debt to spend $3,000 more than their income each year vs. investing $3,000 each year in a diversified portfolio? Assume 9% interest on debt and 7% return on the investment.

Answer 1

If the couple spends $3,000 each year, at the end of 25 years they would be indebted by $254,103

If the couple invests $3,000 each year, at the end of 25 years they would be indebted by $254,103

The difference = $443,850

Step-by-step explanation:

We would calculate the future values of the ordinary annuities using the following formula

FV = A
`[((1+r)^(N) -1)/(r) ]`

Scenario 1 : The couple spends $3,000 each year

A = -3,000

N = 25

r = 9%

FV = -3000
`[((1+0.09)^(25) -1)/(0.09) ]` = -$254,103

Scenario 2 : The couple invests $3,000 each year

A = 3,000

N = 25

r = 7

FV = 3000
`[((1+0.07)^(25) -1)/(0.07) ]` = $189,747

The difference between a couple going into debt if they spend vs. if they invest = $189,747 - (-$254,103) = $443,850