Question

A $21,000 ordinary life insurance policy for a 23-year old female can be obtained for annual premiums of approximately $200. This type of policy (ordinary life) would pay a death benefit of $21,000 in exchange for the annual premium paid during the lifetime of the insured person. If the average life expectancy of a 23-year old female is 63 years, what interest rate establishes equivalence between cash outflows and inflows for this type of insurance policy? Assume all premiums are paid on a beginning-of-year basis and that the last premium is paid on the 62th birthday. The interest rate which establishes equivalence between cash outflows and cash inflows is year. (Round to three decimal places.) 1% per

Answer 1

Number of premium paid till 62nd birthday = 40

Premium amount paid = $200 per year in the start of the period

Since the premium is paid in the beginning of the year, then it is the case of annuity due.

Let, IRR = R

Then,

Future value of the premium paid = 21000

(200*((1+R)^40 - 1)/R)*(1+R) = 21000

At R = 5%

Future value of premiums = $25367.95

At R = 4%

Future value of premiums = $19765.31

As per the method of interpolation,

R = 5% - ((25367.95 - 21000)/(25367.95-19765.31))*(5%-4%)

R = 4.22%