Question

The Lopez family has come to you for advice on life insurance cover to protect their family. Sanjay Lopez, aged 40, is a plumber and his wife, Sarah, aged 35, is a hairdresser. Both work full-time. They have two children: Linda, aged two (2), and Jasper, aged four (4).

Sanjay earns $45,000 and Sarah earn $20,000 and they currently only save $100 per month.

1. If Sanjay was to die, Sarah wants to provide monthly income of $4,500 to their family during the dependency period of their children until the youngest reaches age 18. However, when the youngest child has reached age 18, Sarah would then like to cover $3,250 per month for her life expectancy (age 85) to supplement her income.

Assuming an interest rate of 7% (compounded monthly), inflation at 1.5% (adjusted monthly), what is the total capital requirement needed for income for Sarah in the event of Sanjay’s death?

ALSO, assume Sarah would like this payment to begin at the start of each month from month 1.

Answer 1

Assumming that if Sanjay dies, savings of $100 per month will not be needed or practicable, we are focussing on 4500 per month savings only.

We must divide the entire period into two parts -

a) 16 years until Linda turns 18

b) 34 years when Sarah turns 85.

All the payments are assumed to bade made at the beginning of each month from the beginning of month 1 means at t= 0.

We must discount the cash flows needs on a monthly basis to construct a portflio today which can satisfy our requirements for next 50 years. Discount rate to be sued will be monthly rate after accounting for inflation. Since discount rate and inflation both ate given in monthly compounded format, we can easily calculate monthly rate to be used in calculation =

It comes to be 0.71% approx = 8.5/12.

Now we must pull the cash flows sequentially to arrive at capital sum required to made today or insurance sum assured to be purchased today.

Part 1 - Calculate present value of 3250 for 408 months using 0.71% in BGM mode in BA II plus calculator. It comes to be 435288.

Part 2 - Calculate present value of 4500 for 192 months using 0.71%. Also calculate the PV of 435288 above along with.

Final answer comes to be 586113. If Sarah invets this sum today, it will fulfill her desires of montly cash flows of 4500 for 16 years and 3250 for 34 years therafter assumming cash flows are received at beginning of each period.

She need to buy an annuity due plan with initial investment of 586113 today which will fetch her 4500 for 16 years and 3250 for next 34 years.