Question

2) A motorcycle is for sale for $26,000. The dealer is willing to sell on the following terms: No down payment, pay $ 440 at the end of each of the firs four months; pay $ 840 at the end of each month after until the loan has been fully repaid. At an interest rate of 12% annual interest rate compounded monthly, how many $ 840 payments will be required?

Answer 1

Solution:

There ore two streams of cash-flows. First is $440 per month for first 4 month and then $840 per month till the end of the loan.

So, we will calculate the present worth of both the cash streams.
Monthly interest rate = 12%/12 = 1% (Since the payment is made monthly)

Number of periods for $440 payment = 4

Number of periods for $840 payment = n (We assume it as it needs to be found)

$26,000 = $440 * (P/A, 1%, 4) + $840*(P/A, 1%, n)*(P/F, 1%, 4)

$26,000 = $440 * (3.902) + $840 * (P/A, 1%, n) * (0.9610)

$26,000 - $1,716.88 = $840 * (P/A, 1%, n)'(0.9610)

(P/A, 1%, n) = $24,283.12 / ($840*0.9610)

(P/A, 1%, n) = 30.082

n = 36 (approximately)

Note: You need to search for "n" under P/A for 1% in compounded interest table. It's approximately 36 months.