Question

Suppose you take out a car loan of $10,000 with an interest rate of 12% compounded monthly. you will pay off the loan over 48 months with equal monthly payments.
a) what is the monthly interest rate?
b) what is the amount of the equal monthly payment?
c) what is the interest payment for the 20th payment?
d) what is the total interest paid over the life of the loan?

Answer 1

Answer:

a) 1% per month

2) 263.34 dollar per month

3) interest will be of 64,03‬ in the 20th payment

d) total payment: 2,640.32

Explanation:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 10,000

time 48

a) monthly rate: 12% annual / 12 months per year = 1% = 0.01

$10000 \div \frac{1-(1+0.01)^{-48} }{0.01} = C$

b) C  $ 263.338

amortization at the 1st payment:

263.34 - 10,000 x 0.01 = 163.34

at the 20th payment:

163.34 x 1.01^20 = $199.3058

interest: cuota - amortization = 263.34 - 199.31 = 64,03‬

d) 263.34 x 48 - 10,000 = 2.640,32‬