4-C
Section 4C
Loan Payments, and Credit
Cards
Pages 250-264
4-C
Loan Basics
The principal is the amount of money
owed at any particular time.
Interest is charged on the loan principal.
4-C
Suppose you borrow $1200 at an annual interest rate of APR = 12%
Show the balance of the loan if you pay only the interest due for 6 months.
Month
Prior
Principal
Interest
.12/12 =
1%
Payment
toward
Principal
Total
Payment
1
$1200
$12
$0
$12
$1200
2
$1200
$12
$0
$12
$1200
3
$1200
$12
$0
$12
$1200
4
$1200
$12
$0
$12
$1200
5
$1200
$12
$0
$12
$1200
6
$1200
$12
$0
$12
$1200
BAD IDEA
New Principal
4-C
Suppose you borrow $1200 at an annual interest rate of APR = 12%
Show the balance of the loan if you pay $200 toward principal, plus interest
for 6 months.
Month
Prior
Principal
Interest
.12/12 =
1%
Payment
toward
Principal
Total
Payment
New Principal
1
$1200
$12
$200
$212
$1000
2
$1000
$10
$200
$210
$800
3
$800
$8
$200
$208
$600
4
$600
$6
$200
$206
$400
5
$400
$4
$200
$204
$200
6
$200
$2
$200
$202
$0
VARYING PAYMENT AMOUNTS
4-C
Suppose you borrow $1200 at an annual interest rate of APR = 12%
Show the balance of the loan if you pay $200 for 6 months.
INSTALLMENT LOAN
Month
Prior
Principal
Interest
1%
Payment
toward
Principal
Total
Payment
New Principal
1
$1200
$12
$188
$200
$1012
2
$1012
$10.12
$189.88
$200
$822.12
3
$822.12
$8.22
$191.78
$200
$630.34
4
$630.34
$6.30
$193.70
$200
$436.64
5
$436.64
$4.37
$194.63
$200
$242.01
6
$242.01
$2.42
$197.58
$200
$44.43
decreasing
increasing
4-C
Loan Basics
The principal is the amount of money
owed at any particular time.
Interest is charged on the loan principal.
To pay off a loan, you must gradually pay
down the principal. Each payment should
include all the interest plus some amount
that goes toward paying off the principal.
4-C
Suppose you want to pay off a loan with regular
(equal) monthly payments in a certain amount of
time. Use Loan Payment Formula (pg 252)




APR 
P

n

PMT =
(nY )

APR 

1  1 +


n


PMT = equal regular payment
P = starting loan principal (amount borrowed)
APR = annual percentage rate (as a decimal)
n = number of payment periods per year
Y = loan term in years
4-C
Suppose you borrow $1200 at an annual interest rate of APR = 12%
How much should you pay each month in order to pay off the loan in 6 months.




APR 
P

n

PMT =
(nY )

APR 

1  1 +


n






.12 
1200 

12

PMT =
(120.5)

.12 

1  1 +


12


CALCULATOR
4-C
PMT =
1200  .01
1  1 + .01

CALCULATOR
PMT =
PMT =
12
1  .942045235...
12
.057954765...
PMT = $207.06
( 6 )


4-C
The Loan Payment Formula (pg 252) can be used for
• student loans
• fixed rate mortgages
• credit card debt
• auto loans
More Practice . . .
4-C
A student loan of $25,000 at a fixed APR of 10% for 20 years
a) Determine the monthly payment.
b) Determine the total payment over the term of the loan.
c) Determine how much of the total payment over the loan term
goes to principal and how much to interest.




.10 
25,000 

12

PMT =
(12 20)

.10 

1  1 +


12


= $241.26
CALCULATOR
Total Payment: $241.26 × 12 × 20 = $57,902.40
Principal Payment: $25,000
Interest Payment: $57,902.40 – $25,000 =
$32,902.40
4-C
A home mortgage of $100,000 with a fixed APR of 8.5% for 30 years.
a) Calculate the monthly payment.
b) Calculate the portions of the payments that go to principal and
to interest during the first 3 months. Use a table.




.085 
100000 

12

PMT =
(1230)

.085 

1  1 +


12


= $768.91
Month
Prior
Principal
Total
Payment
Interest
0.7083%
Payment
toward
Principal
New Principal
1
$100,000
$768.91
$708.33
$60.58
$99,939.40
2
$99,939.40
$768.91
$707.90
$61.01
$99,878.39
3
$99,878.39
$768.91
$707.47
$61.44
$99,816.95
4-C
Suppose you have a credit card balance of $2500. The credit card
APR is 18% and you want to pay it off in 1 year. Determine the monthly
payment assuming you make no more credit card purchases.




.18 
2500 

12

PMT =
(121)


.18 
1  1 +

12 

= $229.20
Total Payment: $229.20 ×12 = $2750.40
Principal Paid: $2500
Interest Paid: $2750.40 – $2500 = $250.40
4-C
You need to borrow $10,000 to buy a car and you determine
that you can afford monthly payments of $220. The bank
offers three choices:
a 3 year loan at 7%,
a 4 year loan at 7.5% or
a 5 year loan at 8%.
Which option is best for you?
4-C
You need to borrow $10,000 to buy a car and you determine that you can
afford monthly payments of $220. The bank offers three choices:
a 3 year loan at 7%,




.07 
10,000 

12

PMT =
(123)


.07 
1  1 +

12 

= $308.77
$308.77 × 12 × 3 = $11,115.79
4-C
You need to borrow $10,000 to buy a car and you determine that you can
afford monthly payments of $220. The bank offers three choices:
a 4 year loan at 7.5% or




.075 
10,000 

12

PMT =
(12 4)


.075 
1  1 +

12 

= $241.79
$241.79 × 12 × 4 = $11,605.90
4-C
You need to borrow $10,000 to buy a car and you determine that you can
afford monthly payments of $220. The bank offers three choices:
a 5 year loan at 8%.




.08 
10,000 

12

PMT =
(125)

.08 

1  1 +


12


= $202.76
$202.76 × 12 × 5 = $12,165.60
4-C
You need to borrow $10,000 to buy a car and you determine that you can
afford monthly payments of $220. The bank offers three choices:
a 3 year loan at 7%,
$308.77
a 4 year loan at 7.5% or
$241.79
a 5 year loan at 8%.
$202.76
$308.77 × 12 × 3 = $11,115.79
$241.79 × 12 × 4 = $11,605.90
$202.76 × 12 × 5 = $12,165.60
Which option is best for you?
4-C
Home Mortgages may be more complicated:
• interest rate (lower)
• down payment
• closing costs
•direct fees
• points (each point is 1% of the loan amount)
4-C
You need a loan of $80,000 to buy a home. In each of the two choices,
calculate your monthly payments and total closing costs.
Choice 1: 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point.
Choice 2: 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points.
Choice
Monthly
Payment
1
$545.74
2
$518.88
Closing
Cost
(direct)








.0725
12
PMT =
(1230)


.0725

1  1 +

12 

80,000 
Closing
Cost
(points)
Total
Closing
Costs
Total
Costs




.0675 
80000 

12

PMT =
(1230)

.00675 

1  1 +

12 

4-C
You need a loan of $80,000 to buy a home. In each of the two choices,
calculate your monthly payments and total closing costs.
Choice 1: 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point.
Choice 2: 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points.
Choice
Monthly
Payment
1
$545.74
2
$518.88
Closing
Cost
(direct)








.0725
12
PMT =
(1230)


.0725

1  1 +

12 

80,000 
$545.74 12  30  $196,466.4
Closing
Cost
(points)
Total
Closing
Costs
Total
Costs




.0675 
80000 

12

PMT =
(1230)

.00675 

1  1 +

12 

$518.88 12  30  $186,796.8
4-C
You need a loan of $80,000 to buy a home. In each of the two choices,
calculate your monthly payments and total closing costs.
Choice 1: 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point.
Choice 2: 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points.
Choice
Monthly
Payment
Closing
Cost
(direct)
Closing
Cost
(points)
1
$545.74
$1200
$800
2
$518.88
$1200
$2400
$545.74 12  30  $196,466.4
$80,000  .01  $800
Total
Closing
Costs
Total
Costs
$518.88 12  30  $186,796.8
$80,000  .01 3  $2400
4-C
You need a loan of $80,000 to buy a home. In each of the two choices,
calculate your monthly payments and total closing costs.
Choice 1: 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point.
Choice 2: 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points.
Choice
Monthly
Payment
Closing
Cost
(direct)
Closing
Cost
(points)
Total
Closing
Costs
Total
Costs
1
$545.74
$1200
$800
$2000
196,466 + 2000
= $198,466
2
$518.88
$1200
$2400
$3600
186,797 + 3600
=$190,397
$545.74 12  30  $196,466.4
$80,000  .01  $800
$518.88 12  30  $186,796.8
$80,000  .01 3  $2400
4-C
Homework:
Pages 265-267
#16, 28, 30, 40, 44, 46