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.

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