Question

You borrow $20,000 to purchase a car. The interest rate is 7.5%. The loan is for 10 years. What is the total amount payed? How much would the payment be each month?

Answer 1

• $28,488 repaid
• $237.40 monthly

Explanation:

The monthly payment on a loan is given by the amortization formula. The total amount repaid is the product of the monthly payment and the number of payments made.

The amortization formula is ...

A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . . principal P, interest rate r, t years

For the loan values given here, this is ...

A = 20,000(0.075/12)/(1 -(1 +0.075/12)^(-12·10)) ≈ 237.40

The total repaid over 120 payments is ...

$237.40 × 120 = $28,488

The total amount paid is $28,488. The monthly payment is $237.40.

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Additional comment

The payment and total paid can be computed using a suitable calculator, spreadsheet, or app. The attached picture is from an Android version of a TI-84 calculator. It comes with a built-in set of financial functions, similar to those found in a spreadsheet.

Answer 2

$35,000

$291.67

Explanation:

Assuming that this loan uses simple interest, the equation for this problem will be A=P(1+rt). In this formula: A is the total amount paid, P is the initial amount, r is the rate in decimal form, and t is the time in years.

First, set up the equation by plugging the known values into the formula.

• A = 20,000(1+0.075*10)

Next, uses this information to find A

• A = 35000

This means that the total amount paid was $35,000.

Next, find the monthly payments. Using the time in years, we can figure out that this loan was paid over 120 months. Additionally, the monthly payment was equal for each month. This means that to find the monthly payment, simply divide the total amount by the number of months.

• 35000/120 ≅ $291.67

Each month, approximately $291.67 was paid.