Question

Linda's husband has just passed away and she is entitled to $100,000 insurance benefit. She chooses to receive the benefit annually over 15 payments, with the first payment immediately. Suppose the interest rate that her benefit gets is 4%, but the insurance company can actually invest the money at 5%. How much is the insurance company making (in terms of present value) by paying out the benefit in installments instead of in a lump sum?

Answer 1

PV of annuity for making pthly payment-Annuity Due
P = PMT+PMT x (((1-(1 + r) ^- (n-1))) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Annuity from insurance company will make up the PV of 100,000 @ 4%
100,000	= PMT+PMT * (((1-(1 + 4%) ^- (15-1))) / 4%)
100,000	= PMT+PMT * 10.56312
Per year payment=	100000/11.56312)
Per year payment=	8,648.18
Insurance company can make investments @ 5% so PV of such payments @ 5%
PV=	= 8648.18+8648.18* (((1-(1 + 5%) ^- (15-1))) / 5%)
PV=	94,253.44
Net money made by investment company= 100000-94253.44
	5,746.56