Financial Mathematics
Credit and Loans:

Simple Interest and Flat Rate Loans:

A flat rate loan is one where flat or simple interest is charged on an amount borrowed or principal for the term of the loan. Interest is always charged on the full amount of the loan.

I = Prn
P = principal r = rate per period expressed as a decimal n = number of periods

E.g. Phil borrowed $4000 for three years at 8%p.a. (per annum) (flat rate)
a) What is his interest?
b) What is the total repaid?
c) What are the monthly repayments?

Solution:
a) 4000x8/100x3
Interest=$960

b) Total Repaid: interest + principal
=960+4000
=$4960

c) Monthly repayments:
=4960÷36 (36 is the number of months is 3yrs)
=137.777……
=137.78

Buying on Terms:

Time payment- agreement to pay for goods over a certain period of time
This is also called a hire purchase as the customer actually hires (borrows) the good until they are paid off.
Goods can be reposed if payments are failed to be paid
Deferred Payment Plan- deposit, ‘interest-free period’,

E.g. Jem borrowed $200 at $120 per month for two years. He also paid $300 deposit

A) What was the cash price of the item
=$2300
B) What did he pay in total?
= 120x24+300
=$3180
C) What was the flat interest rate?
= Int= 3180-2300
=$880
=Rate: I=PRN
=880=2000xrx2 (2 means years of interest rate in % p.a.) r=880÷2000÷2 r=0.22 (x100 to find %)
=22% p.a.

Reducing Balance Loan:

Reducible interest
Interest is calculated on the balance still owing, not on the total principal borrowed with flat rate interest
Interest calculated one period at a time
Shortcut- Calculator, operations between = signs get repeated on the calculator
e.g. 5000= x1.09-800 = Ans=Ans=Ans etc. Push equals require amount of times.

E.g. 1) Teri borrows $5000 at 9% reducible interest. If she pays $800 per year, show the first four years balances.
Solution: (Big R means Repayment)
Year
(P) Starting balance
P+Int.
(P+I-R) End Payment
1
5000
5000x1.09=5450
5450-800=4650
2
4650
4650X1.09=5068.50
5068.50-800=4268.5
3
4268.50
=4652.6
=3852.6…
4
3852.6
=4199.4…
=3399.404…

Published Loan Repayment tables:

- What banks uses to calculate large loans

E.g. using table in textbook page 90.

Mr. and Mrs. Pitt obtain a premium home loan of $370,000 at 7%p.a. reducible interest for a term of 20yrs find:

I) the monthly repayment:
Monthly repayment for $1000=7.75
Monthly repayment for $370,000=370x$7.75 = $2867.50

II) The total amount repaid:
=$2867.50x20x12 =$688,200

III) The total interest paid
Interest Paid=total amount repaid-amount borrowed
=4688,200-$370,000 =$318,200

Credit Card Payments:

Two types of credit cards:
No interest-free period and no annual fee at a lower interest rate
An interest-free period and an annual fee- account is paid in full before the period
Ends otherwise interest is charged from the date of purchase
The due date on a statement is when the interest-free period ends.

E.g. 1) Manual has a credit card with no interest-free period and interest rate of 14% p.a. He makes the following purchases for the period 1 August to 31 August:

2 August Dinner Set $65.5
16 August Pair Trousers $85.00
23 August Haircut $24.00
26 August Diner $36.80
29 August White Shirt $32.00 a) What is the total amount of his purchases? Total purchases=$65.50, $85.00, $24.00, $36.80, $32.00 = $243.30
b) Manuel pays his account in full on 3 September. How much does he pay?
Interest is charged on each purchase from the date of purchase until the date payment is received. For example the dinner set is bought on 2 August and paid for on 3 September.
Number of days=29+3= 32
Interest rate per annum= 14%
Interest rate per day= 14/36500

Purchase Amount
No. of days interest
Interest to 3 September ($)
$65.00
32
65.00x14/36500x32=0.8048
$85.00
32-14 =18
85.00x14/36500x18=0.5875
$24.00
11
=0.1013
$36.80
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