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Rajesh would like to buy his first car and the one he has his eye on is \$25,000, plus an extra 13% HST for a total price of \$28,250. The dealership has a deal for \$0 down payment and charges 2.79% interest on the loan. Rajesh plans to make car loan payments weekly and has accepted the maximum loan repayment period of 8 years.How much will his weekly care loan payment be?

How much will he have paid to the dealership by the time his loan is paid off?

How much interest will be paid?

Feb 1, 2022

#1
+1

Not POSITIVE of this scenario

Present value of ordinary annuity

PV = C * ( 1-(1+i)-n ) /i         i = .0279 / 12        n = 8 yr * 12 mos = 96       PV = 28250       find 'C'

C = payments = \$  328.67

Total payments = 96 * 328.67 =  \$ 31552.58         interest =   31552.58 - 28250 = \$ 3302.58

Feb 1, 2022
#2
+1

EP: This is just the calculation of ordinary weekly loan payment over a period of 8 years, or: 8 x 52 weeks==416 weeks. The only uncertainty is the compounding period of the interest rate of 2.79%. But for this question, will take it as being compounded weekly to agree with the weekly payments:

N=8*52; R=0.0279/52;PV=28250; PMT=PV*R*((1 + R)^N) / ((1 + R)^(N) - 1)

PMT==\$75.79 weekly

\$75.79  x  416 weeks ==\$31,528.64 - amount paid to car dealership over a period of 8 years.

\$31,528.64  -  \$28,250 ==\$3,278.64 - total interest paid over a period of 8 years.

Feb 1, 2022
#3
+1

Yah.....I manged to mix weekly and MONTHLY payments ....here is my corrected:

Present value of ordinary annuity

PV = C * ( 1-(1+i)-n ) /i         i = .0279 / 52      n = 8 yr * 52 wks = 416       PV = 28250       find 'C'

C = payments = \$ 75.787

Total payments = 416 * 75.787 =  \$ 31527.43         interest =   31527.4 - 28250 = \$ 3277.43

ElectricPavlov  Feb 1, 2022
#4
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Thanx for finding my mistake ! ElectricPavlov  Feb 1, 2022
#5
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i need the answer in two decimal places

far987  Feb 1, 2022
#6
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Wellllll..... round it to two decimal places.....you SHOULD know how to do THAT!!! ElectricPavlov  Feb 1, 2022