Simple InterestSimple InterestPart 1Part 1

Financial MathsFinancial Maths

SIMPLE INTEREST SIMPLE INTEREST (or flat rate (or flat rate interest)interest)

The simple interest formula is given to The simple interest formula is given to you on the HSC formula sheet you on the HSC formula sheet

I = PrnI = Prnwherewhere I = the interestI = the interest P = initial quantity P = initial quantity

(principal)(principal) r = percentage interest r = percentage interest

rate per period expressed rate per period expressed as a decimalas a decimal

n = number of time n = number of time periods.periods.Example:

Find the amount of simple interest incurred when you have borrowed $80 at 9% p.a. for 2 years.

What is the total amount to be paid on this loan?

Example: Find the amount of simple interest incurred when you have borrowed $80 at 9% p.a. for 2 years.What is the total amount to be paid on this loan? First identify all the information you have been First identify all the information you have been

given:given: P = 80P = 80 r = 9% = 0.09r = 9% = 0.09 n=2n=2

Substitute these values into the simple interest Substitute these values into the simple interest formula: I=Prnformula: I=Prn I = 80 x 0.09 x 2 = 14.4I = 80 x 0.09 x 2 = 14.4

Therefore the amount of interest incurred on the Therefore the amount of interest incurred on the loan is $14.40loan is $14.40

Amount to be repaid = Principal + Amount to be repaid = Principal + Interest (i.e. A = P + I)Interest (i.e. A = P + I) Total = 80 + 14.40 = 94.40Total = 80 + 14.40 = 94.40

Total amount to be repaid is $94.40Total amount to be repaid is $94.40

Finding the interest rateFinding the interest rate In some questions you will need to find the interest rate.In some questions you will need to find the interest rate. To do this you will need to transpose the formula.To do this you will need to transpose the formula.

Example:Example: On a loan of $5 000, Ken paid $1 800 On a loan of $5 000, Ken paid $1 800 interest over 3 years. What is the rate of interest per interest over 3 years. What is the rate of interest per annum?annum? Again, start by identify all the information you have been given.Again, start by identify all the information you have been given. P = 5 000 I = 1 800 n = 3P = 5 000 I = 1 800 n = 3 Substitute these values into the simple interest formula I = PrnSubstitute these values into the simple interest formula I = Prn

1 800 = 5 000 x r x 31 800 = 5 000 x r x 3 1 800 = 15 000 x r1 800 = 15 000 x r r = 1 800 ÷ 15 000r = 1 800 ÷ 15 000 r = 0.12 or 12% (0.12 x 100)r = 0.12 or 12% (0.12 x 100)

The annual rate of interest is 12%The annual rate of interest is 12%

Flat rate loansFlat rate loans A flat rate loan is one where flat (or simple) interest is A flat rate loan is one where flat (or simple) interest is

charged on the amount borrowed for the term of the loan.charged on the amount borrowed for the term of the loan. This type of loan is usually for smaller items such as a This type of loan is usually for smaller items such as a

holiday, computer, DVD or a car. The term of the loan is holiday, computer, DVD or a car. The term of the loan is usually between 1 and 5 years and there may be a small usually between 1 and 5 years and there may be a small charge to cover administration costs. This may be paid in charge to cover administration costs. This may be paid in cash up front or included in the amount borrowed.cash up front or included in the amount borrowed.

Remember:Remember: If you borrow money, you are required to pay it If you borrow money, you are required to pay it back back plus plus interest.interest.

Amount to be repaid = Amount borrowed + interestAmount to be repaid = Amount borrowed + interest Periodical repayment Periodical repayment = = Amount to be repaid Amount to be repaid

No. of periodical repaymentsNo. of periodical repayments

Example: Donna wanted to buy a car stereo for $1500. Her bank offered her a loan at a flat interest rate of 12% p.a. to be repaid in fortnightly instalments over 2 years. The bank charges were stamp duty of $7.50, loan insurance of $8.50 and an establishment fee of $12. If Donna included the bank charges in the amount she borrowed, find:

the total amount to repaythe total amount to repay Write down the information you have been givenWrite down the information you have been given P = 1 500 r= 12% = 0.12 n = 2 P = 1 500 r= 12% = 0.12 n = 2 no. instalments = 52 no. instalments = 52 charges = 7.50 + 8.50 + 12 = 28charges = 7.50 + 8.50 + 12 = 28 Total amount borrowed = 1 500 + 28 = 1528Total amount borrowed = 1 500 + 28 = 1528 Total amount to repay = total amount borrowed + interestTotal amount to repay = total amount borrowed + interest I = Prn = 1 528 x 0.12 x 2 = 366.72I = Prn = 1 528 x 0.12 x 2 = 366.72 Total amount to repay = 1 528 + 366.72 = $1 894.72Total amount to repay = 1 528 + 366.72 = $1 894.72

The fortnightly repayment = 1 894.72 The fortnightly repayment = 1 894.72 ÷ 52 = 36.44÷ 52 = 36.44 Fortnightly repayment = $36.44Fortnightly repayment = $36.44