Question

Your friend just got a five-year car loan for $40,000 with 6% interest rate (APR) and monthly

payments. You explained to her that 6% is too high, and she could have saved a lot of money if she

negotiated with the bank and got 3% instead. How much money would your friend have saved every

month if the rate was 3% instead of 6%?

Answer 1

monthly payment if interest is 6 %

Particulars	Amount
Loan Amount	$             40,000.00
Int rate per month	0.5000%
No. of Months	60

EMI = Loan Amount / PVAF (r%, n)

r is Int rate per month = 6 % / 12 = 0.5 % or 0.005

& n is No. of months = 5 years * 12 = 60

EMI = Loan Amount / PVAF
= $ 40000 / PVAF (0.005 , 60)
= $ 40000 / 51.7256
= $ 773.31

Monthly payment = $ 773.31

PVAF =  [ 1 - [(1+r)^-n]] /r
= [ 1 - [(1+0.005)^-60]] /0.005
= [ 1 - [(1.005)^-60]] /0.005
= [ 1 - [0.74137]] /0.005
= [0.25863] /0.005
= 51.726

monthly payment if interest is 3 %

Particulars	Amount
Loan Amount	$             40,000.00
Int rate per month	0.2500%
No. of months	60

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per month& n is No. of months
= $ 40000 / PVAF (0.0025 , 60)
= $ 40000 / 55.65
= $ 718.75

Monthly payment = $ 718.75

PVAF = [ 1 - [(1+r)^-n]] /r
= [ 1 - [(1+0.0025)^-60]] /0.0025
= [ 1 - [(1.0025)^-60]] /0.0025
= [ 1 - [0.86087]] /0.0025
= [0.13913] /0.0025
= 55.65

Every month savings if she invest at 3 % instead of 6 %

= EMI at 6 % - EMI at 3 %
= $ 773.31 - $ 718.75
= $ 54.56

>> decimals are rounded off