What is your monthly payment for this loan?

Question

In order to buy a new car, you finance $20,000 with no down payment for a term of five years at an APR of 6%. After you have the car for one year, you are in an accident. No one is injured, but the car is totaled. The insurance company says that before the accident, the value of the car had decreased by 25% over the time you owned it, and the company pays you that depreciated amount after subtracting your $500 deductible.

What is your monthly payment for this loan? (Round your answer to the nearest cent.)

Answer 1

20,000-5,000-500=14,500

M= 14,500 x 0.005(1 + 0.005 )60 - 1 elevate to 60 (1 + 0.005)60 elevate to 60

M= 72,5 x 1.34885 / 0.34885 - 1 = 280.33

Fixed Monthly Installment Formula: M= P x i(1 + i) elevate to n /(1 + i)-1

When you are looking for monthly payment you have to substitute the formula with the information you have

First. Solve the top first and divide by the bottom.

(n) = total Number of months

Monthly Interest Rate: 0.005

M = Monthly

20,000 x 0.25 = 5,000

Deductible: 500

Principal: {P}: 20,000 - 5,000 - 500 = 14,500

Annual Interest Rate: 6% or 0.06

Loan term in Months (n): 5 x 12 = 60

Substitution: M = 14,500 x 0.005 {1+ 0.005 } 60

Divided By: {1 + 0.005 } 60 - 1

M = 14,500 x 0.005 { 1.34885}

Divided By: 0.34885

Formula: M = P ____________________ i {1 + i}n

Divided By { 1 + i }n - 1

Calculate: {1+ i }n = {1.005} 60 = 1.348850

Calculate de Numerator : 14,500 x 0.005 x 1.348850 = 97.7916

Calculate de Denominator : 1.348850 - 1 = 0.348850

Divide : 97.7916 By 0.348850 = 280.3256

Elevated to the 60th power = The value of 1.005 is 1.348850

6% or 0.06: Yearly interest

0.06 / 12 = 0.005 : Monthly inerest

/ = divided by

The Monthly Payment is: $280.33

P = Principal 14,500

I = Interesr 6% or 0.06

Years = 5

12 = months in 1 year 5 x 12 = 60 months