Question

A city must replace a piece of equipment fifteen years in the future. It is estimated that in fifteen years the required piece of equipment will cost $37,500. If the city can lock in a fifteen-year certificate of deposit that earns 4% annually, how much money will the town need to invest in this certificate of deposit today to ensure they will have $37,500 in fifteen years? What if the certificate of deposit earns 12% annually

The city from question 14 decides it cannot afford this single lump sum deposit today and instead elects to annually contribute to an annuity. The equipment still is estimated to cost $37,500 and the interest rate is still 4% annually or 12% annually. Given this, how much will the town’s annual annuity payment be to ensure they have $37,500 in fifteen years at the 4% interest level and the 12% interest level? Show your math.

Answer 1

FV = 37500
Rate = 4%
PV of the certificate of deposit at 4% = 37500/(1+4%)¹⁵ =20822.42
PV of the certificate of deposit at 12% = 37500/(1+12%)¹⁵ =6851.22

Annual Payments at 4% = 37500/(1-(1+4%)^-15)/4%= 3372.79
Annual Payments at 12% = 37500/(1-(1+12%)^-15)/12%=5505.91

Please Discuss in case of Doubt

Best of Luck. God Bless
Please Rate Well