Question

A service contract for a video projection system costs $80 a year. You expect to use the system for six years. Instead of buying the service contract, what would be the future value of these annual amounts after six years if you earn 3 percent on your savings?

Answer 1

The future value of the annual amounts after six years, earning an annual rate of return of 3% is $517.47

What is the future value of an ordinary annuity of $80 per year for six years earning a rate of 3% annually?

Note that the $80 that would have been paid for the video projection system would be invested at the end of each year, in other words, we would invest an equal amount every year for six years, hence, the future value formula of an ordinary annuity is the most appropriate to determine the value of the savings after six years

FV=annual savings*(1+r)^N-1/r

annual savings=$80

r=rate of return=3%

N=number of annual savings for 6 years=6

FV=$80*(1+3%)^6-1/3%

FV=$80*(1.03)^6-1/0.03

FV=$80*(1.194052296529-1)/0.03

FV=$80*0.194052296529/0.03

FV=$517.47

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