Question

Asma plans to retire in exactly 20 years. After retirement her goal is to invest in a fund that will allow her to receive Rs. 20,000 at the end of each year for the next 30 years after retirement. She will be able to earn 11% per year during the 30-year retirement period. How large a fund will Asma need when she retires in 20 years to provide for the 30-year, Rs, 20,000 retirement annuity?

Answer 1

Answer:

Asma will need Rs, 173,875.85.

Explanation:

Since Asma will be receiving payments at the end of each year, the relevant formula to use to calculate the amount she will need she retires is the formula for calculating the present value of an ordinary annuity as follows:

PV = P × [{1 - [1 ÷ (1 + r)]^n} ÷ r] …………………………………. (1)

Where;

PV = What the present value of the amount needed be in 20 years or the amount Asma will nee when she retires in 20 years = ?

P = yearly payment = Rs, 20,000

r = interest rate = 11%, or 0.11

n = number of years = 30

Substitute the values into equation (1) to have:

PV = Rs, 20,000 × [{1 - [1 ÷ (1 + 0.11)]^30} ÷ 0.11]

PV = Rs, 20,000 × 8.69379257346612

PV = Rs, 173,875.85

Therefore, Asma will need Rs, 173,875.85 when she retires in 20 years to provide for the 30-year, Rs, 20,000 retirement annuity.