Question

Just before his first attempt at bungee jumping, John decides to buy a life insurance policy. His annual income at age 30 is $38,000, so he figures he should get enough insurance to provide his wife and new baby with that amount each year for the next 35 years. If the long-term interest rate is 6.7%, what is the present value of John's future annual earnings? (Round your answer to the nearest cent.)

$___________

Your answer is correct. Rounding up to the next $50,000, how much life insurance should he buy? (Round your original answer to the nearest $50,000.)

$_________

Answer 1

Sol:

Annual income (PMT) = $38,000

Interest rate (r) = 6.7%

Period (nper) = 35 years

a) Present value (PV) of John's future annual earnings can be determine by using PV function in excel.

PMT	-38000
Interest rate	6.70%
nper	35
Present value	$508,556.56

Therefore Present value (PV) of John's future annual earnings is $508,556.56

Present value (PV) of annuity can also be determined with the following formula:

Present value (PV) of annuity = C x (1 – [1/(1 + r)^n] / r)

Present value (PV) of annuity = 38000 x (1 – (1/(1 + 6.70%)^35)) / 6.70%)

Present value (PV) of annuity = 38000 x (1 – (1/(1.0670)^35) / 0.0670)

Present value (PV) of annuity = 38000 x 13.38306

Present value (PV) of annuity = $508,556.56

b) $508,556.56 rounding up to the next $50,000, John should buy $550,000 as life insurance.

Working