# 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:**

- Interest ($) = Principal ($) × Interest Rate (as a decimal) × Time (years)
- I = P × R × T
- Total = Principal + Interest
- T = P + I
- Principal = Interest ÷ (Rate × Time)
- P = I ÷ (R × T)
- Rate = Interest ÷ (Principal × Time)
- R = I ÷ (P × T)
- Time = Interest ÷ (Principal × Rate)
- T = I ÷ (P × R)

**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% p.a. (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?

**Answer:**

(a) Interest

= Principal × Interest Rate × No. of Years

= $1000 × 5% × 3 years

= 1000 × 0.05 × 3

= $150

(b) Total

= Principal + Interest

= $1000 + $150

= $1150

## Example Two - Simple Interest on Loan

Alan owes $800 on his credit card. The bank interest is 8 ^{3}⁄_{4} % (8.75%) p.a. 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?

**Answer:**

(a) I = P × R × T

= 800 × 0.0875 × ^{1}⁄_{12}

= $5.83

(b) Total

= Principal + 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 5 ^{3}⁄_{8} % 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?

**Answers**
**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.

**Answer:**

Principal

= Interest ÷ (Rate × Time)

= $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.

**Answer:**

Interest Rate

= Interest ÷ (Principal × Time)

= $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.

**Answer:**

Time

= Interest ÷ (Principal × Rate)

= $288 ÷ ($2400 × 0.08)

= 1.5 years

## Questions - Finding P, R, T

**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 6 ^{3}⁄_{4} % p.a.

**Answers**
**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?

**Answer:**

(a) Total

= $40 × 52 weeks × 2 years

= $4160

(b) Extra Interest

= $4160 – $4000

= $160

(c) Interest Rate

= I ÷ (P × T)

= $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?

**Answer:**

(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 × T)

= $480 ÷ ($4800 × 2yr)

= 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?

**Answers**

(a) $2700

(b) $15300

(c) $21420

(d) $3420

(e) 7.45%