Question

Problem 6-4 (LO6.1) A service contract for a video projection system costs $245 a year. You expect to use the system for three years. Instead of buying the service contract, what would be the future value of these annual amounts after three years if you earn 5 percent on your savings? Use Exhibit 1-B. (Round time value factor to 3 decimal places and final answer to 2 decimal places.) Future value

Answer 1

Given that the service contract costs $245 per year:
Interest earned on savings=5%
Given that the system will be used for 3 years. So, we will calculate the future values for 3 years.
We need to calculate the future value of the annual amounts after 3 years:

Future value=Present value*(1+rate of interest)^number of years
Here, present value for all years will be the service contract cost=$245 per year

Year 1:
The interest will be calculated for 2 years.
Future value=$245*(1+5%)^2=$245*(1.05)^2=$270.1125

Year 2:
Interest will be calculate for 1 year.
Future value=$245*(1+5%)^1=$245*(1.05)^1=$257.25

Year 3:
Interest will be calculate for 0 year or no interest will be calculated here at it is the last year of calculation and the amount will be considered as the future value after three years.
Future value=$245*(1+5%)^0=$245*(1.05)^0=$245

We will get the total future value after three years by adding the future values of each year.
So, future value of the annual amounts after three years=$270.1125+$257.25+$245=$772.3625 or $772.36 (Rounded up to 2 decimal places)