A person wants to buy a life insurance policy which would yield a large enough sum of money to provide for 20 annual payment of $50,000 to surviving members of the family. The payments would begin 1 year from the time of death. It is assumed that interest could be earned on the mum received from the policy at a rate of 8 percent per year
compounded annually (a) What amount of insurance should be taken out aao na to ensure the desired annuity? (b) How much interest will be earned on the policy benefits over the 20-year period?
Answers
(a) The amount of insurance should be taken out aao na to ensure the desired annuity is $573,750.
(b) The interest earned on the policy benefits over the 20-year period will be $1,675,167.50.
Given:
- rate of interest = 8%
- a life insurance policy with a payout large enough to cover 20 payments of $50,000 per year to the family's remaining members
- One year after the death, the payments would start.
To find:
(a) The amount of insurance should be taken out aao na to ensure the desired annuity = ?
(b) The interest earned on the policy benefits over the 20-year period will be = ?
Solution:
(a) We may use the present value calculation for an annuity to calculate the amount of insurance that should be purchased to guarantee the desired payment:
PV equals PMT times ((1 - (1 + r)(-n)) / r).
Where:
- The annuity's current value is known as PV.
- $50,000 is the annual payment amount for PMT, and 8% is the annual interest rate (r is equal to 0.08 in decimal form).
- 20 payments total, or n, have been made.
When we use the formula with these values, we get:
PV = 50000 * ((1 - (1 + 0.08)^(-20)) / 0.08) PV = 50000 * ((1 - 0.158) / 0.08)
PV = 50000 * (11.475)
PV = $573,750
(b) In order to guarantee the desired annuity, $573,750 worth of insurance should be purchased.
- Using the future value method, we can determine the amount of interest that will be collected over the course of the 20-year period on the policy benefits:
FV = PV * (r + 1)n
Where:
- The annuity's FV, or the sum of all payments made throughout the course of the 20-year period,
- The annuity's present value (PV) is $573,750, and the annual interest rate (r) is 8% (converted to a decimal, so r = 0.08).
- 20 years are in n, the number of years.
Inputting these values into the formula yields the following results:
FV = 573750*1+0.08*20 FV = 573750*4.66096 FV = $2,675,167.50
As a result, $2,675,167.50 less $1,000,000 (the initial cost of the insurance policy) equals $1,675,167.50 in interest that will be generated on the policy benefits over the course of 20 years.
Hence, the amount of insurance should be taken out aao na to ensure the desired annuity is $573,750 and the interest earned on the policy benefits over the 20-year period will be $1,675,167.50.
#SPJ1