AskSia

Plus

You are considering taking out a car loan for $5,000. The loan has an annual int...

Jan 29, 2024

You are considering taking out a car loan for $5,000. The loan has an annual interest rate of 6% and a term of 5 years. Calculate the total amount you will have paid by the end of the loan term, assuming you make regular monthly payments. Also, how much of that amount is interest?

Answer

The total amount paid by the end of the loan term is

5,930.00, and the total interest paid is

930.00.

Solution

Loan Payment Formula: The monthly payment can be calculated using the formula for an annuity:

P = \frac{rPV}{1 - (1 + r)^{-n}}

where

P

is the monthly payment,

r

is the monthly interest rate,

PV

is the present value of the loan, and

n

is the total number of payments

Calculating Monthly Interest Rate and Number of Payments: The monthly interest rate is

\frac{6\%}{12} = 0.005

(or 0.5%), and the total number of payments for a 5-year loan is

5 \times 12 = 60

payments

Calculating Monthly Payment: Substituting the values into the annuity formula gives us

P = \frac{0.005 \times 5000}{1 - (1 + 0.005)^{-60}} \approx 96.66

So, the monthly payment is approximately $96.66

Calculating Total Payment and Interest: The total amount paid over the term of the loan is

60 \times 96.66 = 5,799.60

, and the total interest paid is

5,799.60 - 5,000 = 799.60

Key Concept

Time Value of Money

Explanation

The time value of money concept is used to calculate the monthly payment and the total interest paid on a loan, taking into account the interest rate and the number of payments.

◊From a Microeconomics perspective, the related question could be: - How do interest rates and loan terms affect the total amount paid and interest paid on a car loan?⍭ Generate me a similar question◊