Question

A 11-year annuity pays $1,400 per month, and payments are made at the end of each month. The interest rate is 14 percent compounded monthly for the first Five years and 12 percent compounded monthly thereafter.

  

Required:

What is the present value of the annuity?

$97,790.41

$95,872.95

$131,778.37

$1,150,475.38

$93,955.49

Answer 1

This problem can be broken in 2 parts

Part 1 - annuity at 14% interest rate for 5 years
Part 2 - annuity at 12% interest rate for 6 years

Part 1 -

P = 1400
r = 14% annual or 0.14/12 monthly
Number of periods n = 5*12 = 60 months
=> PV = P(1-(1+r)^-n)/r = 1400(1-(1+0.14/12)^-60)/(0.14/12) = $60167.82

Part 2 -

P = 1400
r = 12% annual or 0.12/12 monthly
Number of periods n = 5*12 = 72 months
=> PV at Year 5 = P(1-(1+r)^-n)/r = 1400(1-(1+0.12/12)^-72)/(0.12/12) = $71610.55
PV at Year 0 = 71610.54/(1+0.14/12)⁶⁰ = $35705.12

Hence, Value of Annuity = 60167.82 + 35705.12 = $95872.94

Hence, (b) is the correct option