Question

You took a loan to buy a new car. The monthly interest rate on the loan is 1.5% and you have to pay $240 every month for 60 months

1)What is the Present value of the Cash flows if its an ordinary annuity?

2)What is the future value of cash flows if its an ordinary annuity?

3)What is the present value of the cash flows if its an annuity due?

4)What is the future value of cash flows if its an annuity due?

Answer 1

1)

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

Present value of ordinary annuity = 240 * [1 - 1 / (1 + 0.015)^60] / 0.015

Present value of ordinary annuity = 240 * [1 - 0.409296] / 0.015

Present value of ordinary annuity = 240 * 39.380269

Present value of ordinary annuity = $9,451.26

2)

Future value of ordinary annuity = Annuity * [(1 + r)^n - 1] / r

Future value of ordinary annuity = 240 * [(1 + 0.015)^60 - 1] / 0.015

Future value of ordinary annuity = 240 * [2.44322 - 1] / 0.015

Future value of ordinary annuity = 240 * 96.214652

Future value of ordinary annuity = 23,091.52

3)

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

Present value of annuity due = (1 + 0.015) * 240 * [1 - 1 / (1 + 0.015)^60] / 0.015

Present value of annuity due = 1.015 * 240 * [1 - 0.409296] / 0.015

Present value of annuity due = 1.015 * 240 * 39.380269

Present value of annuity due = $9,593.03

4)

Future value of annuity due = (1 + r) * Annuity * [(1 + r)^n - 1] / r

Future value of annuity due = (1 + 0.015) * 240 * [(1 + 0.015)^60 - 1] / 0.015

Future value of annuity due = 1.015 * 240 * [2.44322 - 1] / 0.015

Future value of annuity due = 1.015 * 240 * 96.214652

Future value of annuity due = 23,437.89