The Reliance Volunteer Fire Company wants to take advantage

The Reliance Volunteer Fire Company wants to take advantage of a state program to save money to purchase a new fire truck. The truck will cost $310,000, and members of the finance committee estimate that with community and state contributions, they can save $6,500 per month in an ordinary annuity paying 10.4% annual interest. How long will it take to save for the truck?

Solution

Rate of Interest = 10.4%/12 =
Future Value = 310,000
Let n be the number of periods
FV = Annuity * ((1+r)ⁿ - 1)/r
310,000 = 6500 * ((1+ 10.4%/12)ⁿ-1)/10.4%/12
1.413333 = (1+ .104/12)ⁿ

Applying log on both sides
n = log(1.413333) /Log(1 +0.104/12)
n =40.09 months
Years =40.09/12 = = 3.34 years

Best of Luck. God Bless