Question

How much life insurance should a person have if he/she desires to provide the following income for his/her beneficiaries?

a) $30,000 per year for 20 years beginning immediately (assume 6% rate)

b) $30,000 per year for 15 years. Beginning immediately (assume 6% rate)

Answer 1

Part a

Given :-

Amount to be received annually = $30,000

number of years = 20

Interest Rate = 6% per annum

Solution

The amount of Insurance should be equal to the "Present value of $30,000 discounted at 6% per annum for 20 years.

Amount of Insurance = Fixed amount to be received *[1+ PVAF(6%, 19 Years)]

NOTE:-

1)PVAF = Present Value Annuity Factor

2) For Formula for calulating PVAF (6%, 19years) , refer attached image.

Therefore,

Amount of Insurance = $30,000 *(1+ 11.158)

Amount of Insurance = $3,64,740 (approx)

Part b

Given :-

Amount to be received annually = $30,000

number of years = 15

Interest Rate = 6% per annum

Solution

The amount of Insurance should be equal to the "Present value of $30,000 discounted at 6% per annum for 15 years.

Amount of Insurance = Fixed amount to be received *[1+ PVAF(6%, 14 Years)]

Amount of Insurance = $30,000 * (1+ 9.295)

Amount of Insurance = $ 3,08,850 (appox)

Annexure for calculating PVAF for 15 years