Question

Angelo takes out a 48-month loan for $40,000 at an interest rate of 12% per year to purchase a car. The loan payments are made monthly. The amount of the loan that is still remaining after 1 year is closest to？

Answer 1

Particulars	Amount
Loan Amount	$             40,000.00
Int rate per Month	1.0000%
No. of Months	48

EMI = Loan Amount / PVAF (r%, n)
Where
r is Int rate per Month = 12 % / 12 = 1% or 0.01
n is No. of Months = 48 months
= $ 40000 / PVAF (0.01 , 48)
= $ 40000 / 37.974
= $ 1053.35

Particulars	Amount
Loan Amount	$    40,000.00
Int rate per Month	1.0000%
No. of Months	48
Outstanding Bal after	12 months
EMI	$      1,053.35
Payments Left	36 months

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r

r = Int Rate per period = 1% or 0.01
n = Balance No. of periods = 36 months
= $ 1053.35 * [ 1 - ( 1 + 0.01 ) ^ - 36 ] / 0.01
= $ 1053.35 * [ 1 - ( 1.01 ) ^ - 36 ] / 0.01
= $ 1053.35 * [ 1 - 0.698925 ] / 0.01
= $ 1053.35 * [ 0.301075 ] / 0.01
= $ 31713.74

Amount of the loan after 1 years = $ 31713.74

Please comment if any further assistance is required.