Question

Beverly and Kyle Nelson currently insure their cars with separate companies, paying $620 and $640 a year. If they insured both cars with the same company, they would save 15 percent on the annual premiums What would be the future value of the annual savings over 10 years based on an annual interest rate of 8 percent? Use Exhibit 1-B. (Do not round Intermediate calculations. Round time value factor to 3 decimal places and final answer to 2 decimal places.) Future value of annual savings

Answer 1

The new premiums for both of them would be:

Premium new = Premiumoid x (1 – 15%)

Premium new = 620 + 640) x (1 – 15%)

Premium new = 1071

While the old premium was 640+620 = 1260

So the savings will be 1260-1071 = $189 a year

The future value of this annuity at the end of 10 years is calculated as follows:

We are given the following information:

PMT	$                  189.00
r	8.00%
n	10.00
T	1

We need to solve the following equation to arrive at the required FV

FV = PMTX (1+r)" - 1 FV = 189 x (1 +0.08)10 - 1 0.08 FV = 2737.96

So the FV is $2737.96