Calculating Interest on Loans
• The Annual Percentage Rate (APR) may or
may not be the same as the rate stated on the
contract
• The difference is a result of how interest was
calculated
• Ways to calculate interest
• Add-On
• Simple Interest on the Unpaid Balance
• Discount Interest
Definitions
• Periods
• the number of payments you will make during the
life of the loan
• Total Interest
• the amount of total interest that will paid during the
entire life of the loan
Definitions
• Principal Payment
• the amount of ONLY principal that will paid
during a given period
• Interest Payment
• the amount of ONLY interest that will paid
during a given period
• Periodic Payment
• the total principal plus interest that will paid
during a given period
Add-On Interest
• Interest is calculated on the original loan for the
entire period of the loan.
• The periodic payment will be the same amount
each period
• Very easy to calculate
Add-On Interest Formulas
• Total Interest
• Amount * Rate * Years
• Interest Payment
• Total Interest / number of periods
• Principal Payment
• Loan Amount/number of periods
• Periodic Payment
• Principal Payment + Interest Payment
Add-On Interest Example
Assume we have a $12,000 loan at 6% add-on
interest for 2 years with semi-annual payments.
A. How many periods are there in this loan?
2 yrs * Twice a Year = 4 periods
B. What is the total interest charged?
Amount * Rate * Years
12,000 * .06 * 2 = $1440
Add-On Interest Example
C. What is the Interest Payment?
Total Interest / # of periods
1440 / 4 = $360 in Interest
D. What is the Principal Payment?
Loan Amount / # of periods
12,000 / 4 = $3,000 in Principal
E. What is the total Periodic Payment?
Principal + Interest
$3,000 + $360 = $3360
Simple Interest on the Unpaid
Balance
• We no longer assume that the full amount is
borrowed for the entire time period.
• Instead, we take into account our principal
payments
• Thus, we get a lower unpaid balance each
period to calculate interest on for that period
• Can do two different types
• Equal Principal Payment
• Equal Total Payment
Simple Interest on the Unpaid
Balance - Equal Principal Payment
• Principal Payment
• Loan Amount / # of payments
• Interest Payment
• Unpaid Balance of Loan * Rate * Year Proportion
• Periodic Payment
• Principal Payment + Interest Payment
Simple Interest Equal Principal
Example
Assume you have a $12,000 loan at 6% simple annual
interest on the unpaid balance for 2 years with semiannual payments.
A. How many periods are there?
2 yrs * 2 times a year = 4 periods
B. What is the principal payment each period?
Loan Amount / # of periods
12,000/4 = $3,000
Simple Interest Equal Principal
Example
Fill in the information from the last slide:
Beginning Balance of Loan, Periods, Principal Payment
Period
Beginning
Balance
1
12,000
Principal Payment Interest Payment
3,000
2
3,000
3
3,000
4
3,000
Totals
Ending Loan
Balance
Simple Interest Equal Principal
Example
To find the ending Balance: Beginning Balance - Principal Payment
Period
Beginning
Balance
Principal
Payment
1
12,000
3,000
9,000
2
9,000
3,000
6,000
3
6,000
3,000
3,000
4
3,000
3,000
0
Totals
Interest
Payment
Ending Loan
Balance
Simple Interest Equal Principal
Example
To find the interest payment:
Beginning Loan Balance * Rate * Year Proportion
Period 1 = 12,000 * .06 * 6.12 = $360
Period 2 = 9,000 * .06 * 6/12 = $270
Period
Beginning
Balance
Principal
Payment
Interest
Payment
Ending Loan
Balance
1
12,000
3,000
360
9,000
2
9,000
3,000
270
6,000
3
6,000
3,000
180
3,000
4
3,000
3,000
90
0
Totals
Simple Interest Equal Principal
Example
Add up the totals to find total interest
Period
Beginning
Balance
Principal
Payment
Interest
Payment
Ending Loan
Balance
1
12,000
3,000
360
9,000
2
9,000
3,000
270
6,000
3
6,000
3,000
180
3,000
4
3,000
3,000
90
0
XXXXXX
12,000
900
XXXXXX
Totals
True Rate of Interest
• Truth and Lending Act
• Show borrowers total finance charges
• Provide the APR - Annual Percentage Rate
• The APR may or may not be the same as
the rate stated on the contract, depending
upon the way that interest was calculated.
• The APR is also known as the True Rate of
Interest
TRI
• True Rate of Interest (TRI)
TRI =
2*m*I
LP * (N+1)
m = the number of payments in one year
I = total interest and finance charges
N = total number of payments
LP = Loan Proceeds
TRI Example
What is the true rate of interest on a $12,000 loan at
6% add-on interest for 2 years with semi-annual
payments?
2*m*I
TRI =
LP * (N+1)
TRI =
2 * 2 * $1440
12,000 * (4+1)
TRI = 9.6%