Question

A loan of $20,000 to purchase a car at annual nominal rate of interest of 6% compounded monthly will be paid back through monthly installments over 5 years,
(a) with the 1st installment to be made 1 month after the release of the loan. What is the

monthly installment?

(b) with the 1st installment to be made Right after the release of the loan. What is the monthly installment?

(DO NOT USE EXCEL)

(answer for A is $386.66 and answer for B is $384.77 *I THINK*) Please show work for support on answer.

Answer 1

Answer a.

Amount borrowed = $20,000
Annual interest rate = 6.00%
Monthly interest rate = 0.50%
Period = 5 years or 60 months

Let monthly payment at the end of each month be $x

$20,000 = $x/1.005 + $x/1.005^2 + … + $x/1.005^59 + $x/1.005^60
$20,000 = $x * (1 - (1/1.005)^60) / 0.005
$20,000 = $x * 51.725561
$x = $386.66

Monthly payment = $386.66

Answer b.

Amount borrowed = $20,000
Annual interest rate = 6.00%
Monthly interest rate = 0.50%
Period = 5 years or 60 months

Let monthly payment at the beginning of each month be $x

$20,000 = $x + $x/1.005 + … + $x/1.005^58 + $x/1.005^59
$20,000 = $x * 1.005 * (1 - (1/1.005)^60) / 0.005
$20,000 = $x * 51.984189
$x = $384.73

Monthly payment = $384.73