Question

1. You have taken out a loan of $32,000 to buy a new Saturn. The loan will be paid off in monthly instalments starting in one month over the next 4 years (48 payments). The interest rate on the loan is 8.25% per year. The bank doesn’t tell you, but it is compounded quarterly. (a) Find the amount of the monthly loan payments. (b) The amount owed immediately after the 30th payment is

Answer 1

(a) $ 1,056.57

(b) $ 15,753.45

Step-1:Calculation of equivalent monthly interest rate
(1+i)^n	=	(1+i)^n		Where,
(1+i)^3	=	(1+0.020625)^1	Quarterly Interest rate	=	8.25%/4
(1+i)^3	=	1.020625			=	0.020625
1+i	=	1.020625	^(1/3)
1+i	=	1.00682827
i	=	0.00682827
So,
Equivalent monthly interest rate	=	0.00682827
Step-2:Monthly Loan payment calculation
Monthly Loan payment calculation	=-pmt(rate,nper,pv,fv)	Where,
		= $   1,056.57			rate	=	0.020625
					nper	=	48
					pv	=	$       32,000
					fv	=	0
Step-3:Calculation of money owed after 30th payment
Money owed after 30th payment	=pv(rate,nper,pmt,fv)		Where,
		= $ 15,753.45			rate	=	0.020625
					nper	=	18
					pmt	=	$ -1,056.57
					fv	=	0