Question

A couple wants to have an annuity of 25,000 payable at the beginning of each year for 10 years. If they have 20 years to save for that annuity, how much must be saved from their annual year-end bonus? Assume a 5% interest rate.

Answer 1

Corpus required for annuity of 25,000 for 10 years at the beginning of year =

N PV = Ax

A = 25,000

r = 5% and N =10

PV = 25,000x [1-1/(1+0.05)^10)/0.05

PV = 25,000 x 7.72173492918481

PV = 193043.37322962

Since, we need annuity at the beginning of year, corpus required = 193043.37322962 * (1+0.05)

= 202695.541891101

Now, amount to be saved for each year to build corpus of 202695.541891101 =

Pmt = FV xi/ ((1 + i)" - 1)

FV = 202695.541891101

i = 5% and n = 20

Pmt = 202695.541891101 x 0.05 / ((1+0.05)^20 - 1)

Pmt = 202695.541891101 x 0.0302425871906913

Pmt = 6130.03759880606

Hence, savings required at the end of year = 6130.03759880606