- People default on simple interest loans too often, so real financial institutions want regular payments.
- This is called an installment loan
- For something like a car, where there is a fixed number of payments, they are called fixed installment loans
- For a credit card, they are called open-ended installment loans
- This section will deal with fixed installment loans.
- The term finance charge refers to the total amount the borrower must pay, including interest and fees.
- The book "defines" finance charge to be the same thing as interest.
- This is not true, but it will do.
- The total installment price is the sum of all of the monthly payments, along with the down payment, if any.
- When working with installment loans we deal with the following
- principal (p)
- interest or finance charge (i)
- rate (r)
- time (t)
- number of payments (n)
- monthly payment (m)
- We can use this formula
p*r/n
m = ---------------
1-(1+r/n)^(-nt)
- Or we can use a table
-
- Example: number 12, page 641
Juan Avalos paid $7000 for a new
central air-conditioning unit for
his house. He paid 20% as a down
payment and financed the balance
with a 36 month fixed installment
loan with an APR of 5%.
a. Determine Juan's finance charge
b. Determine Juan's monthly payment
1. Compute the Down payment
$7,000 x .2 = $1,400
2. Compute the Amount Financed
$7,000 - $1,400 = $5,600
3a. Compute amount financed and monthly payment
Use formula
p = 5600
r = 5%
t = 36/12 = 3 years
n = 12
m = p(r/n)/(1-(1+r/n)^(-nt))
= 5600(.05/12)/(1-(1+.05/12)^(-3*12)
= 167.84
So the total amount of the loan is
167.84 * 36 = 6042.24
So the finance charge is
6042.24 - 5600 = 442.24
Use the table
look up 36 months at 5% interest
7.90
This is the finance charge per 100 financed.
We need to find the number of $100 financed
5600/100 = 56
So the finance charge is
56 * 7.90 = 442.40
The total for the loan is p+i
442.40 + 5600 = 6,042.40
The monthly payment is
6,042.40/36 = 167.84
- Sometimes we need to work backwards
- Example page 641 number 14
Ilga Ross purchased a new computer on a monthly
purchase plan. The computer sold for $1495.
Ilga paid 5% down and $64 a month for 24 months.
a. What finance charge did Ilga pay?
b. What is the APR to the nearest 1/2 percent
1. Compute the down payment:
1,495 x .05 = 74.75
2. Compute the amount financed
1,495-74.75 = 1,420.25
3. Compute the Amount of the loan
64 * 24 = $1,536
4. Compute the finance charge
1,536 - 1,420.25 = 115.75
5. Compute the number of $100
1,420.25 / 100 = 14.205
6. Compute the finance charge per hundred
115.75/14.205 = 8.148 = 8.15
7. Use finance charge per hundred and months to find APR
7.5%
- Sometimes we also pay a loan off early
- To do this we need to compute Unearned Interest
- u = nPV/(100+V)
- n is the number of remaining monthly payments
- P is the monthly payment
- V is the value from the apr table for r and n
- Example problem 18 page 642
Jeslie Ann Hernandez has a 48-month installment
loan with a fixed monthly payment of $83.81.
The amount she borrowed was $3,500. Instead
of making her 18th payment, Jeslie Ann
is paying the remaining balance on the loan.
a. Determine the APR of the installment loan.
b. How much interest will Jeslie Ann save by paying
off the loan early?
c. What is the total amount due to pay off the loan?
1. Compute The Amount of the loan
$83.81 * 48 = $4,022.88
2. Compute the finance charge
4,022.88 - 3500 = 522.88
3. Compute the number of $100
3500/100 = 35
4. Compute the finance charge per $100
522.88/35 = 14.94
5. Look up the APR based on FC/$100 and months
7.0%
6. Find n
48 - 18 = 30
7. Find V
Lookup 30, 7% -> 9.30
8. Compute u
u = nPV/(100+V)
= 30*83.81*9.30/109.30
= 213.93
9. Compute Payoff
payoff = this month + all other months - u
= 83.81 + 30*83.81 - 213.93
= 2,384.18