Question

If you invest $96 per month (starting next month) every month for 36 years, and you can earn 11% per year (compounded monthly), how much will you have at the end of 36 years? Round to the nearest cent.

If the most you can afford each month on a car payment is $393, the applicable discount rate is 4.1% per year, and an auto-loan is for 5 years paid monthly, what's the most expensive car you should purchase today assuming you finance the whole car (no money down)?

Answer 1

Question 1

Future value of Annuity = A [((1+r)ⁿ-1) / r]

Where

A - Annuity payment = 96

r - rate per period = .11/12

n - no. of periods = 36*12 = 432

Future value of Annuity = 96* [((1+(.11/12))^432 -1) / (.11/12)]

= 96* [(51.5194888143 -1) / 0.00916666666]

= 96*5511.21696557

= 529076.83

Question 2

Present value of Annuity = A*[(1-(1+r)^-n)/r]

Where

A - Annuity payment = 393

r - rate per period = .041/12

n - no. of periods = 5*12 = 60

Present value of Annuity = 393* [(1-(1+(.041/12))^-60)/(.041/12)]

= 393* [(1-0.81493201424)/(.041/12)]

= 393*54.1662397346

most expensive car = 21287.33