Question

Problem 6-4 You have just purchased a new car for $60,000. You pay no money down and will make 60 equal monthly payments starting next month. The interest rate is 10% per year. Amortize the first three months of your loan.
can you also explain how to get the first payement ?

Answer 1

monthly payment formula:

P*r*(1+r)^n / [(1+r)^n-1]

here,

P=60,000

r = 10% per year

=>10%* 1 /12 =>0.833333% per month...(since we have to make monthly payments, we need to find out the monthly rate).

=>0.0083333

n = 60 months.

monthly payment = 60,000*0.008333*(1.0083333)^60 / [(1.0083333)^60-1]

=>499.998*1.64530861/0.64530861

=>$1,274.82.

now,

amortization table for first three payments.

payment number	beginning loan balance	interest (beginning balance * 0.83333%)	payment made	principal repaid (payment made - interest)	closing balance (beginning balance - principal repaid)
1	60,000	500	1274.82	(1274.82-500)=>774.82	(60,000-774.82)=>59,225.18
2	59,225.18	(59225.18*0.83333%)=>493.54	1274.82	(1274.82-493.54)=>781.28	(59,225.18-781.28)=>58,443.90
3	58,443.90	(58443.90*0.83333%)=>487.03	1274.82	(1274.82-487.03)=>787.79	(58443.90-787.79)=>57,656.11