Question

Kentaro and riku sakaguchi have jobs and contribute to the household expenses according to their income. Kentaro contributes 75% of the expenses, and Riku contributes 25% Currently, their household expenses are $30,000 annually (hint assume payments at the beginning of the year; i.e., BEG mode). Kentaro and Riku have three children. The youngest child is 12, so they would like to ensure that they maintain their current standard of living for at least the next eight years. They feel that the insurance proceeds could be invested at five percent. In addition, to covering the annual expenses, they would like to make sure their children has $30,000 available for college. If Kentaro was to die, Riku would go back to school part time to upgrade her training as a nurse. This would cost $28,500. They have a mortgage on their home with a balance of $175,000. How much life insurance should they purchase for kentaro sakaguchi?

Answer 1

Answer: Amount of life insurance will the sum of the following values:

1. current value of $ 30000.00 less 7500 i.e 22500 (share of Kentaro) for next 8 years i.e

Present value of annuity due: C×[1−(1+r)^−n/r​]×(1+i)

30000*(1-(1+0.05)^-8/0.05)*(1+0.05)

=$152,693.40

2. since it is not mentioned that when they wil require $ 30000 for college fee, it is assumed that they will require same at the end of 8th year according to which it has current value of :

PV=FV/(1+r)^n

=$ 20,304.57

3. finally 28500+175000 as they wil require same immediately.

=$ 203,500.00

thus total insurance value is 1+2+3= $ 3,76,497.97