Question

Sara Wald died, leaving to her husband Benno an insurance policy contract that provides that the beneficiary (Benno) can choose any one of the following options: a) 55,000 immediate cash b) 4,000 every 3 months payable at the end of each quarter for 5 years c) 18,000 immediate cash and 1,800 every 3 months for 10 years, payable at the beginning of each 3-month period d) 4,000 every 3 months for 3 years and 1,500 each quarter for the following 25 quarters, all payments payable at the end of each quarter Using the interest rate of 2.5 per quarter, compounded quarterly, which option would you recommend that Benno exercise? Show your computations!

Answer 1

Solution:

In order to recommend best optoin to Benno, we have to calculate present value of amount to be received for each option and option which give higher present value will be recommended.

Option a: Immediate cash of $55,000:

Present value of benefits = $55,000

Option b: 4,000 every 3 months payable at the end of each quarter for 5 years:

Total period = 5*4 = 20 periods

Quarterly interest rate = 2.5%

Present value of benefits = $4,000 * cumulative PV factor of ordinary annuity at 2.5% for 20 periods

= $4,000 * 15.58916 = $62,356.65

Option c: 18,000 immediate cash and 1,800 every 3 months for 10 years, payable at the beginning of each 3-month period

Total period = 10*4 = 40 periods

Quarterly interest rate = 2.5%

Present value of benefits = $18,000 + $1,800 * cumulative PV factor for immediate annuity for 40 period at 2.50%

= $18,000 + $1,800 * 25.73034 = $64,314.62

Option d: 4,000 every 3 months for 3 years and 1,500 each quarter for the following 25 quarters, all payments payable at the end of each quarter:

Total period = 3*4 + 25 = 37 quarters

Quarterly interest rate = 2.5%

Present value of benefits = $4,000 * cumulative PV factor at 2.50% for first 12 periods + $1,500 * cumulative PV factor at 2.50% from 13th period to 37th period

= $4,000 * 10.25776 + $1,500 * 13.69955

= $61,580.39

From above, present value of benefits is higher under option c i.e. $64,314.62, Therefore benno should exercise option of "18,000 immediate cash and 1,800 every 3 months for 10 years, payable at the beginning of each 3-month period"