# Simple Interest

When you save money in a bank account, the bank pays you interest.

When you borrow money from a bank, you must pay both the loan and the interest to the bank.

The Principal is the amount either saved or borrowed.

Simple Interest is also called Flat Interest.

Simple Interest Rules are:

• Simple Interest (\$) = Principal (\$) × Interest Rate (as a decimal) × Number of Years (time)
• I = P × i × n
• Total = Principal + Simple Interest
• Total = P + I
• Principal = Simple Interest ÷ (Interest Rate × Number of Years)
• P = I ÷ (i × n)
• Interest Rate = Simple Interest ÷ (Principal × Number of Years)
• i = I ÷ (P × n)
• Number of Years = Simple Interest ÷ (Principal × Interest Rate)
• n = I ÷ (P × i)

Remember:

• "per" means "divide"
• "cent" means "100"
• "of" means "multiply"

## Example One - Simple Interest on Savings

Alana has \$1000 in her bank account. The bank pays interest of 5% per annum (each year).
(a) What interest will the bank over a period of 3 years?
(b) How much will she have altogether in her bank account after 3 years?

(a) Simple Interest
= Principal × Interest Rate × Number of Years
= P × i × n
= \$1000 × 5% × 3 years
= 1000 × 0.05 × 3
= \$150

(b) Total
= Principal + Simple Interest
= \$1000 + \$150
= \$1150

## Example Two - Simple Interest on Loan

Alan owes \$800 on his credit card. The bank interest is 834 % (8.75%) per annum There is no interest-free period on the credit card.

(a) What interest will he have pay for one month?
(b) How much will he have altogether after one month?

(a) I = P × i × n
= 800 × 0.0875 × 112
= \$5.83

(b) Total
= Principal + Simple Interest
= \$800 + \$5.83
= \$805.83

## Questions - Simple Interest

Q1. Fred earns 5.25% interest p.a. on his savings of \$760.
(a) What simple interest is earned over 30 months?
(b) What is the total amount that he will have after 30 months?

Q2. Freda owes \$49 on her credit card which has an interest rate of 538 % p.a. There is no interest-free period on her credit card.
(a) How much interest does she owe after one month?
(b) What is the total amount owing after one month?

A1. (a) \$99.75 (b) \$859.75
A2. (a) \$0.22 (b) \$49.22

## Example Three - Finding the Principal

The principal is the amount borrowed.

Find the principal if the interest paid is \$100, the interest rate is 5% p.a., and the time of the loan is 4 years.

Principal
= Simple Interest ÷ (Interest Rate × Number of Years)
= \$100 ÷ (0.05 × 4)
= \$500

## Example Four - Finding the Interest Rate of a Loan

Find the interest rate if the interest paid is \$20, the principal is \$250, and the time of the loan is 2 years.

Interest Rate
= Simple Interest ÷ (Principal × Number of Years)
= \$20 ÷ (250 × 2)
= 0.04
= 4%

## Example Five - Finding the Time of a Loan

Find the time of the loan if the interest paid is \$288, the principal is \$2400 and the interest rate is 8% p.a.

Time
= Simple Interest ÷ (Principal × Interest Rate)
= \$288 ÷ (\$2400 × 0.08)
= 1.5 years

## Questions - Finding P, i, n

Q1. Find the principal if the interest paid is \$562.50, the interest rate is 7.5% p.a., and the time of the loan is 18 months.

Q2. Find the interest rate if the interest paid is \$1100, the principal is \$8000, and the time of the loan is 2 years 9 months.

Q3. Find the time of the loan if the interest paid is \$1822.50, the principal is \$2700 and the interest rate is 634 % p.a.

A1. \$5000
A2. 5%
A3. 10 years

## Example Six - Hire Purchase (Buying on Terms) A set of photo-voltaic cells (solar panels) cost \$4000. Instead of paying cash, Teresa Green paid weekly payments of \$40 for 2 years.
(a) How much she pay altogether?
(b) What is the extra interest paid?
(c) What interest rate was paid?

(a) Total
= \$40 × 52 weeks × 2 years
= \$4160

(b) Extra Interest
= \$4160 – \$4000
= \$160

(c) Interest Rate
= I ÷ (P × n)
= \$160 ÷ (\$4000 × 2yr)
= 0.02
= 2%

## Example Seven - Hire Purchase with a Deposit

A greenhouse cost \$6000. Instead of paying cash, Al Pine paid a 20% deposit and 24 monthly payments of \$220.
(a) How much was the deposit?
(b) How much was borrowed?
(c) How much did he pay altogether?
(d) What is the extra interest paid?
(e) What interest rate was paid?

(a) Deposit
= 20% of \$6000
= \$1200

(b) Amount borrowed
= \$6000 – \$1200
= \$4800

(c) Total paid including Deposit
= \$1200 + (\$220 × 24 months)
= \$6480

(d) Extra Interest
= \$6480 – \$6000
= \$480

(e) Interest Rate
= I ÷ (P × n)
= \$480 ÷ (\$4800 × 2 years)
= 0.05
= 5%

## Question - Hire Purchase

An electric car cost \$18000. Instead of paying cash, Sparky paid a 15% deposit and fortnightly payments of \$240 for 3 years.
(a) How much was the deposit?
(b) How much was borrowed?
(c) How much did she pay altogether?
(d) What is the extra interest paid?
(e) What interest rate was paid?   