Question

Matt is saving to buy a new motorcycle. If he deposits ​$65 at the end of each month in an account that pays an annual interest rate of 6.5​%, how much will he have in 24 ​months? Assume that the compounding is being done monthly.

Answer 1

Since, he is making a deposit periodically (monthly), this is an annuity question.
The future value of an annuity is given by FV = P((1 + r/t)^nt - 1) / (r/t)
where:
P is the periodic payment = $65.
r is the annual interest rate = 6.5% = 0.065.
t is the number of payments in one year = 12
n is the number of years = 2 years

Therefore, FV = 65((1 + 0.065 / 12)^(2 x 12) - 1) / (0.065 / 12)
= 65((1 + 0.005417)^24 - 1) / 0.005417
= 65((1.005417)^24 - 1) / 0.005417
= 65(1.1384 - 1) / 0.005417
= 65(0.1384) / 0.005417
= 8.9979 / 0.005417
= 1,661.15

Therefore, at the end of 24 months, Matt will have $1,661.15