- A fixed installment loan is a loan where a set number of payments are made. After these payments, the principal and interest are paid off.
- This is a traditional car loan, signature loan, ...
- To do these types of problems
- We need to compute the finance charge.
- Add the finance charge to the principal
- Divide by the number of payments.
- Table 11.2 presents finance charge per $100 financed.
- Use payments and apr to find the FC/$100
- Divide principal by 100 to find number of $100 financed
- Multiply these two to find total finance charges.
- Example: I borrow $3456 at 6.0% interest and will pay it back in 24 payments. Find the finance charge:
1. Look on the table for 6%, 24 payments -> 6.37
2. Divide 3456 by 100 -> 34.56
3. Multiply 34.56 × 6.37 = 220.15
- Find the monthly payment
Amount Due = Principal + Finance Charge
= 3,456 + 220.15
= 3676.15
Payment = Amount Due / Total Payments
= 3676.15/24
= 153.17
- Example: Marta purchased a truck for $32,000. She paid 30% down and
financed the rest with a 36 month fixed installment loan with an APR of
9.5%. Find the Marta's finance charge and monthly payment.
1. Find the finance charge per $100 (36, 9.5) -> 15.32
2. Find the number of $100
To do this we need the amount financed.
Find down payment 32000 x .3 = 9,600
Find amount financed = 32000-9600
= 22,400
22400/100 = 224
3. Multiply 15.32 × 224 = 3,431.68
Find the total amount
22,400 + 3,431.68 = 25,831.68
Find the monthly payment
25,831.68/36 = 717.55
- Sometimes we need to work backwards
Price = 5200
Down Payment = 900
Amount Number of Payments = 48
Monthly Payment = 100
Find APR
Total Amount = 100 x 48 = 4800
Amount Financed = 5200-900 = 4300
Finance Charge = 4800 - 4300 = 500
Number of $100 financed = 43
Finance Charge per $100 = 500/43 = 11.63
Find 11.63 in the table form 48 months -> 5.5%
- If you pay off an installment loan early, you are not required to pay interest on the principal after you pay off your loan.
- This is called unearned interest
- The actuarial method is used to compute the unearned interest.
- u = (n×P×V)/(100+V)
- u is unearned interest
- n is the number of remaining payments
- P is the monthly payment
- V is the value from the APY table for r% and n months.
- Example:
If a 48 month loan has an APY of 7.5%, with monthly payments of $237, is paid
off in the 30th month. Find the final payment.
1. Compute u
P = 237
n = 48-30 = 18
V = lookup 18, 7.5 -> 6.04
u = 18 × 237 × 6.04 / (100+6.04)
= 242.99
2. Compute Amount To Pay
Current Month + Remaining Months - Unearned Interest
237 + 18*237 - 242.99
= 4,260.01
- Ray took out a 60 month fixed installment loan for $12,000
His monthly payment was 232. He wishes to pay the loan off at his
30th payment. Find the amount he needs to repay.
1. Compute the APR
Find Finance Charge
Find The Total Amount
60 × 232 = 13,920
13,920 - 1200 = 1,920
Find the Finance Charge per $100
1,920/120 = 16
Look up 60, 16 -> 6%
2. Compute Unearned Interest
n = 60-30 = 30
P = 232
V = (lookup 30, 6%) -> 7.94
u = 30 × 232 × 7.94/(100+7.94)
= 511.97
3. Compute Payoff
Current Month + Remaining Months - Unearned Interest
232 + 30*232 - 511.97
= 6680.03