Question

You are considering purchasing a new car and would need to finance $24,000 of the purchase. The dealership will finance the purchase for you for 60 months at an annual interest rate of 2.9%.

a. What is the true interest rate?

b. What is the effective annual interest rate?

c. What is the monthly payment on this fully amortized loan?

Answer 1

Loan amount= $24000

Interest i = 2.9%

1. True interest rate= 1/ (1-i) -1

= 1/ (1- 2.9%) -1

= 1/0.971 -1

= 1.02986 -1

= 0.2986 or 2.99%

2. Effective Interest Rate Formula (compounded monthly) = (1 + i/n) ⁿ – 1

I= 2.9%

N= number of compounding per year, i.e as it is paid monthly. N= 12

EIR= (1+ 0.029/12)¹² -1

= 1.029388-1

= 0.029388 or 2.94%

3. Loan Payment = Amount / Discount Factor or P = A / D

• Number of Periodic Payments (n) = Payments per year times number of years
• Periodic Interest Rate (i) = Annual rate divided by number of payment periods
• Discount Factor (D) = {[(1 + i) ^n] - 1} / [i(1 + i)^n]

Here n= 60

i =2.9/12= 0.24% or 0.0024

D= {[(1 + 0.0024) ^60] - 1} / [0.0024(1 +0.0024)^60]

= 57.79

EMI= 24000/ 57.79 = $430.19