4C Loan Payments, Credit Cards
and Mortgages
principal = amount of money owed
at any particular time
Example: borrow $1200 at APR 12% compounding monthly
(1% per month)
|
prior principal |
interest on prior principal |
payment toward principal |
total payment |
new principal |
| month 1 |
1200 |
1200 * 1% = 12 |
200 |
212 |
1000 |
| month 2 |
1000 |
1000 * 1% = 10 |
200 |
210 |
800 |
| month 3 |
800 |
800 * 1% = 8 |
200 |
208 |
600 |
| month 4 |
600 |
600 * 1% = 6 |
200 |
206 |
400 |
| month 5 |
400 |
400 * 1% = 4 |
200 |
204 |
200 |
| month 6 |
200 |
200 * 1% = 2 |
200 |
202 |
0 |
pay off the loan in 1/2 year.
If you only pay off the interest each month, you will have to pay
forever.
Say we want to pay the same amount every month, some always going
to the principal:
Loan Payment Formula (Instalment Loan)
PMT = [P * APR/n] /
[1 - (1 + APR/n)-nY]
where
P = starting loan principal
PMT = regular payment amount
APR = annual percentage rate
n = number of payment periods per year
Y = loan term in years
-
Given a student loan of $25,000 at an APR of 10% for 20 years. Calculate
the monthly payment,
the total payment over the term of the loan
how much of the total payment goes to the pricipal / interest
Over the time the loan is paid back, the interest portion of the amount
paid every month becomas smaller and the amount paid toward the pricipal
becomes larger.
-
Given a home mortgage of $100,000 with a fixed APR of 8.5%
for 30 years. Calculate
the monthly payment
the portions of the monthly payment that go to principal and interest
in the first three months
Credit Cards
-
Complete the table (APR = 18% annually), initial balance $300:
| Month |
Payment |
Charges |
Interest |
Balance |
| 0 |
|
|
|
$ 300 |
| 1 |
$ 300 |
$ 175 |
$ 300 * 1.5% = $ 4.50 |
$ 179.50 |
| 2 |
$ 150 |
$ 150 |
|
|
| 3 |
$ 400 |
$ 350 |
|
|
| 4 |
$ 500 |
$ 450 |
|
|
| 5 |
$ 0 |
$ 100 |
|
|
| 6 |
$ 100 |
$ 100 |
|
|
| 7 |
$ 200 |
$ 150 |
|
|
| 8 |
$ 100 |
$ 80 |
|
|
Mortgages:
fixed rate is better than variable rate, because it locks in
the payment amount into the future.
-
need a $100,000 loan
Option 1: 30 year loan at an APR of 8%
Option 2: 15 year loan at an APR of 7.5%
same closing costs.
Compute
monthly payments,
total payment
discuss pros / cons
-
need a $80,000 loan
Option 1: 30 year loan at a fixed APR of 8%, closing costs:
$1200, no points
Option 2: 15 year loan at a fixed APR of 7.5%, closing costs
$1200, 2 points
Compute
monthly payments,
total payment
discuss pros / cons
-
You can afford monthly payments of $500. If the current mortgage
rates are 9% for a 30 year fixed rate loan, what loan pricipal can you
afford? If you are required to make a 20% down payment and you have
cash on hand to do it what price home can you afford?