Joe Nautilus has $120,000 and wants to retire. What return must his money earn so he may receive annual benefits of $20,000 for the next 14 years.
a) 12%
b)Between 12% and 13%
c) 14%
d) Greater than 15%
To find the return that Joe Nautilus' money must earn, we can use the concept of present value and annuity.
The present value formula for an annuity is:
PV = PMT x [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value (amount of money Joe Nautilus has)
PMT = Payment (annual benefits Joe Nautilus wants to receive)
r = Interest rate (return that Joe Nautilus' money must earn)
n = Number of periods (number of years Joe Nautilus wants to receive the annual benefits)
From the question, we know that:
PV = $120,000
PMT = $20,000
n = 14
Rearranging the formula to solve for r, we get:
r = [1 - (PV / PMT)]^(-1 / n) - 1
Substituting the given values into the formula, we have:
r = [1 - ($120,000 / $20,000)]^(-1 / 14) - 1
Performing the calculation:
r = [1 - 6]^(-1 / 14) - 1
r = (-5)^(1 / 14) - 1
r ≈ 0.140425 - 1
r ≈ -0.859575
The calculated interest rate is approximately -0.859575. Since negative interest rates are not possible for earning money, we can conclude that Joe Nautilus would need a return greater than 15% (option d) in order to receive annual benefits of $20,000 for the next 14 years.