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

unpaid balance is : $149.99-$50 = $99.99 new balance = 149.99+2.62-50 = $102.61 finance charge = 99.99- 0.21/12= $1.75 new balance = 99.99+1.75 = $101.74 average daily balance method average daily balance= 3399.70/30 = $113.32 finance charge = $ 0.21/12ă—113.32 = $1.98 new balance = $149.99-50+1.98 = $101.97