Answer:
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
Explanation:
We would calculate the future values of the ordinary annuities using the following formula
FV = A [tex][\frac{(1+r)^{N} -1}{r} ][/tex]
Scenario 1 : The couple spends $3,000 each year
A = -3,000
N = 25
r = 9%
FV = -3000 [tex][\frac{(1+0.09)^{25} -1}{0.09} ][/tex] = -$254,103
Scenario 2 : The couple invests $3,000 each year
A = 3,000
N = 25
r = 7
FV = 3000 [tex][\frac{(1+0.07)^{25} -1}{0.07} ][/tex] = $189,747
The difference between a couple going into debt if they spend vs. if they invest = $189,747 - (-$254,103) = $443,850
