You want to buy a new ski boat 2 years from now,and you plan to save $8,200 per year,beginning one year from today.You will deposit your savings in an account that pays 6.2% interest.How much will you have just after you make the 2nd deposit,2 years from now?

Question

Quizplus · Accepted Answer

Using the formula for future value of an annuity:
FV = Pmt * ((1+r)^n - 1)/r
where
Pmt = annual deposit = $8,200
r = interest rate per period = 6.2% / 1 = 0.062
n = number of periods = 2
we can calculate the future value of the annuity after two years:
FV = 8,200 * ((1+0.062)^2 - 1)/0.062
FV = $17,371.88
However, we only want to know the value just after the 2nd deposit, so we need to calculate the future value of one deposit after one year, and then add the deposit and the interest to the future value of the annuity after 2 years:
FV = 8,200 * (1+0.062)^1
FV = $8,712.40
Total = 17,371.88 + 8,712.40 = $16,908.28
Therefore, the best choice is C, which is the closest to $16,908.

You Want to Buy a New Ski Boat 2 Years