Business Math

Business Math

by Shiney John

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What is the formula for calculating the amount for a loan?

​CHAPTER 10.2:MONTHLY PAYMENT AND TOTAL INTEREST

​PAGES 377-378

​Objective of the lesson

• Examine interest fluctuation and monthly payment ·

• Demonstrate to calculate the total amount of interest charged ·

• Compute the amount charged using algebra​

Determining the Monthly Payment and Total Interest​

​Lenders that make mortgage loans charge interest. This is the money the borrower pays for the use of the lender’s money. The interest rate will fluctuate from lender to lender, so it pays to “shop around.”

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Task 1: 

How can you find the interest and the monthly payment?

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What does it means to “shop around” for a mortgage?

Formula

​The formula to determine the monthly payment is:

Monthly Payment = Amount of Mortgage /1,000 × Monthly Payment for $1,000 Loan

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​When you know the monthly payment, you can calculate the total amount paid over the life of the loan using this formula:

Amount Paid = Monthly Payment × Number of Payments

You can calculate the total interest paid over the life of the loan using this formula: Total Interest Charged = Amount Paid – Amount of Mortgage

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​Example 1

​Carol and Adam Burke have applied for a $280,000 mortgage loan at a 9% annual interest rate. The loan is for 30 years, and the Burkes will pay it in equal monthly payments that include interest. What is the total amount of interest charged?

​Step 1: Find the monthly payment. (Refer to Figure 10.1 for the Monthly Payment for a $1,000 Loan table on page 377.)

The value for 9% and 30 years is $8.05.

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Amount of Mortgage/ 1,000 × Monthly Payment for $1,000

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Loan $280,000/ $1,000 × $8.05 = $2,254.00 monthly payment

​Continued

​Step 2: Find the amount paid. Monthly Payment × Number of Payments $2,254.00 × (12 months × 30 years)

$2,254.00 × 360 = $811,440.00 amount paid

Step 3: Find the total interest charged.

Total Interest Charged = Amount Paid – Amount of Mortgage

$811,440.00 – $280,000.00 = $531,440.00

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Use the Monthly Payment for a $1,000 Loan table in Figure 10.1 on page 377.

Find Cameron Bond’s (a) monthly payment, (b) amount paid, and (c) interest charged for a $390,000 mortgage loan at a 5% annual interest rate for 20 years.

​Answer

​a. $2,574 b. $617,760 c. $227,760

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Assessment 1:

Abigail and Curtis Siebert: $270,000 mortgage at 7% for 20 years.

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​Monthly Payment Formula Another way to determine the monthly payment is to use the Monthly Payment Formula introduced in Lesson 8.1, Installment Loans—Monthly Payment and Finance Charge. You can compute the monthly payment on a mortgage loan using this formula: Monthly Payment = pr(1+r) ⁿ/ (1+r)ⁿ –1

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​Where p = Principal, or the amount of the mortgage r = Rate per payment, that is, the mortgage rate divided 12. n = Number of payments required to pay off the loan, that is, the number of years multiplied by 12.

The use of the formula requires a calculator with a y x key.

The formula enables you to determine the monthly payment for numerous mortgage rates and terms.

​Example 2

​Carol and Adam Burke have applied for a $280,000 mortgage loan at a 9% annual interest rate. The loan is for a period of 30 years, and they will pay it in equal monthly payments that include interest. Find the (a) monthly payment, (b) amount paid, and (c) total interest charged.

​​First, r = 9%/ 12 = 0.0075 and n = 30 × 12 = 360 Then, substitute into the formula:

Monthly Payment = pr(1+r) ⁿ (1+r)ⁿ –1

= $280,000(0.0075)(1+.0075)³⁶⁰ (1+.0075)³⁶⁰–1

= $2,100(14.73057612) /14.73057612–1

= $30,934.20986 /13.73057612 = $2,252.943328

The Burkes’ monthly payment is $2,252.94.

The amount paid is $2,252.94 × 360 = $811,058.40.

The total interest charged is $811,058.40 – $280,000 = $531,058.40

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Ramin and Akbar Habil obtained a $98,000 mortgage loan at an annual interest rate of 6.24%. The loan is for a period of 22 years, and the Habils will pay it in equal monthly payments that include interest. Find the (a) monthly payment, (b) amount paid, and (c) total interest charged.

​Answer

a. $683.38 b. $180,412.32 c. $82,412.32​

Multiple Choice

Check the computation is correct or not? Facts: Loan Amount = $100,000 Term = 30 years Annual Interest Rate = 6% Monthly Payment = $100,000 ÷ $1,000 × $6.00 = $600. Amount Paid = $600 × 30 years × 10 payments = $180,000. Total Interest Charged = $180,000 − $100,000 = $80,000.”

• No. It should be 12 payments per year, not 10. Correct results are: Amount Paid = $26,000; Total Interest Charged = $116,000.

• Yes. It should be 12 payments per year, not 10. Correct results are: Amount Paid = $216,000; Total Interest Charged = $116,000.

• No. It should be 12 payments per year, not 10. Correct results are: Amount Paid = $216,000; Total Interest Charged = $116,000.

• No. It should be 12 payments per year, not 10. Correct results are: Amount Paid = $216,000; Total Interest Charged = $16,000.

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Give the important terms of the lesson