Installment Loans―Allocation of Monthly Payment

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Section ObjectiveSection ObjectiveWork out:

• payment to interest

• payment to principal

• new balance

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repayment schedule (p. 294)

A schedule showing the distribution of interest and principal payments on a loan over the life of the loan.

Key Words to KnowKey Words to Know

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Interest = Principal × Rate × Time

Formula 1Formula 1

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Payment to Principal = Monthly Payment – Interest

Formula 2Formula 2

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New Principal =

Previous Principal – Payment to Principal

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Why is it important to get a copy of your repayment schedule?

A Picture Perfect Loan p. 294A Picture Perfect Loan p. 294

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The Coles obtained the loan of $1,800 at 8 percent for 6 months shown in Figure 8.1 on page 294. Show the calculation for the first payment.

What is the interest?

What is the payment to principal?

What is the new principal?

Example 1Example 1

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Find the interest.

Principal × Rate × Time

$1,800.00 × 8% × 1/12 = $12.00

Example 1 Answer: Example 1 Answer: Step 1Step 1

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Find the payment to principal.

Monthly Payment – Interest

$307.08 – $12.00 = $295.08

Example 1 Answer: Example 1 Answer: Step 2Step 2

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Find the new principal.

Previous Principal – Payment to Principal

$1,800.00 – $295.08 = $1,504.92

Example 1 Answer: Example 1 Answer: Step 3Step 3

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Carol Blanco obtained a loan of $6,000 at 8 percent for 36 months. The monthly payment is $187.80. The balance of the loan after 20 payments is $2,849.08.

What is the interest for the first payment?

What is the interest for the 21st payment?

Why is the interest so different for the two payments?

Example 2Example 2

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Find the interest for the first payment.

Principal × Rate × Time

$6,000.00 × 8% × 1/12 = $40.00

Example 2 Answer: Example 2 Answer: Step 1Step 1

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Find the interest for the 21st payment.

Principal × Rate × Time

$2,849.08 × 8% × 1/12 = $18.00

Example 2 Answer: Example 2 Answer: Step 2Step 2

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The interest is much greater for the first payment the 21st payment because the principal is much greater.

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Cathleen Brooks obtained an 18-month loan for $3,200. The interest rate is 15 percent. Her monthly payment is $199.68. The balance of the loan after 6 payments is $2,341.45.

Practice 1Practice 1

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a. What is the interest for the first payment?

b. What is the interest after the seventh payment?

c. How much more goes toward the principal on the seventh payment compared to the first payment?

Practice 1 (cont.)Practice 1 (cont.)

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a. Interest for the first payment: $40.00

b. Interest after the seventh payment: $29.27

c. Amount more that goes toward the principal on the seventh payment compared to the first payment: $10.73

Practice 1 AnswerPractice 1 Answer

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Sam Billings obtained a personal loan for $1,500 at 12 percent for 12 months. The monthly payments on the loan are $133.20. Find the interest, payment to principal, and balance for the first three payments.

Practice 2Practice 2

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a. Interest on first payment?

b. Payment to principal?

c. New principal?

d. Interest after second payment?

e. Payment to principal?

Practice 2 (cont.)Practice 2 (cont.)

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f. New principal?

g. Interest on third payment?

h. Payment to principal?

i. New principal?

Practice 2 (cont.)Practice 2 (cont.)

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a. Interest on first payment: $15.00

b. Payment to principal: $118.20

c. New principal: $1,381.80

d. Interest after second payment: $13.82

e. Payment to principal: $119.38

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f. New principal: $1,262.42

g. Interest on third payment: $12.62

h. Payment to principal: $120.58

i. New principal: $1,141.84

Practice 2 Answer (cont.)Practice 2 Answer (cont.)

Installment Loans―Allocation of Monthly Payments

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