Question

Megan is considering the purchase of a new car. She wants to buy the new Audi A1, which will cost her R347 500. She will finance 90% of the purchase price at an interest rate of 8% per annum, with monthly payments over three years. Interest is compounded monthly. How much money will she still owe on the loan at the end of one year

Answer 1

Cost of car	347,500
Financed portion	90%
Financed portion	312,750
PV of annuity
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	$    312,750.00
PMT = the dollar amount of each annuity payment	To be computed
r = the effective interest rate (also known as the discount rate)	8.30%	(1+8%/12)^12)-1)
i= nominal rate of interest	8.00%
n = the number of periods in which payments will be made	3
PV of annuity=	PMT x (((1-(1 + r) ^- n)) / i)
312750=	Annual payment* (((1-(1 + 8.30%) ^- 3)) / 8%)
Annual payment=	312750/ (((1-(1 + 8.30%) ^- 3)) / 8%)
Annual payment=	$    117,605.38
FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$    117,605.38
r = the effective interest rate (also known as the discount rate)	8.30%
i=nominal Interest rate	8.00%
n = the number of periods in which payments will be made	1
FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / i)
FV of annuity=	117605.38* ((((1 + 8.30%) ^ 1) - 1) / 8%)
FV of annuity=	$    122,014.86
Loan balance after 1 year=	312750*(1+8.30%)-122014.86
Loan balance after 1 year=	$    216,693.24