Simple Interest

Key Ideas

Key Terms

Simple interest: Calculated only on the original principal — the interest does not earn further interest.
years: . Convert months ÷ 12 to get years.
A = P + I: .

Find	Formula	Example
Interest (I)	I = PRT ÷ 100	P=$1000, R=5%, T=3 yr → I=$150
Total amount (A)	A = P + I	$1000 + $150 = $1150
Rate (R)	R = I × 100 ÷ (P × T)	I=$150, P=$1000, T=3 → R=5%
Time (T)	T = I × 100 ÷ (P × R)	I=$150, P=$1000, R=5% → T=3 yr
Principal (P)	P = I × 100 ÷ (R × T)	I=$150, R=5%, T=3 → P=$1000

Hot Tip Time must be in years. If given months, divide by 12 first. For example, 18 months = 18 ÷ 12 = 1.5 years.

Worked Example

Question: Find the simple interest and total amount on $3000 at 4% p.a. for 2 years.

Step 1 — Identify the values.
P = $3000, R = 4, T = 2

Step 2 — Calculate interest.
I = PRT ÷ 100 = 3000 × 4 × 2 ÷ 100 = $240

Step 3 — Find total amount.
A = P + I = $3000 + $240 = $3240

The Simple Interest Formula

Simple interest is calculated only on the original amount borrowed or invested (the principal). The formula is:

I = PRT, where I = interest earned or paid, P = principal (starting amount), R = annual interest rate as a decimal, T = time in years.

Example: You invest $2000 at 5% per year for 3 years. I = 2000 × 0.05 × 3 = $300. The total amount after 3 years is A = P + I = $2000 + $300 = $2300.

Total Amount Formula

The total amount (final balance) is: A = P + I = P + PRT = P(1 + RT).

Example: $5000 invested at 4% per annum for 2.5 years. A = 5000(1 + 0.04 × 2.5) = 5000 × 1.1 = $5500.

Note: time must always be in years. If the time is given in months, divide by 12 first. 18 months = 18/12 = 1.5 years.

Rearranging for P, R, or T

If you need to find the principal, rate, or time, rearrange I = PRT:

P = I / (RT). R = I / (PT). T = I / (PR).

Example: How long does it take for $1000 to earn $150 in interest at 6% per year? T = 150 / (1000 × 0.06) = 150 / 60 = 2.5 years.

Example: What rate is needed to earn $200 interest on $4000 over 2 years? R = 200 / (4000 × 2) = 200 / 8000 = 0.025 = 2.5% per year.

Real-World Applications

Simple interest applies to some short-term personal loans, hire purchase agreements, and some savings accounts. It is simpler than compound interest because the interest does not grow over time — each year you earn or owe exactly the same amount.

For a loan: you pay the interest on top of repaying the principal. A $3000 loan at 8% simple interest for 18 months costs I = 3000 × 0.08 × 1.5 = $360 in interest. Total repaid = $3360.

Common mistake: Forgetting to convert the interest rate from a percentage to a decimal. If the rate is 5%, use R = 0.05 in the formula, not R = 5. Using R = 5 gives an answer 100 times too large. Also check whether time is given in months — always convert to years before substituting into I = PRT.

Mastery Practice

Use the formula I = PRT ÷ 100 to find the simple interest for each row. Fluency

	Principal (P)	Rate (R % p.a.)	Time (T years)
(a)	$1 000	5%	3
(b)	$2 500	6%	4
(c)	$800	3%	2
(d)	$4 500	8%	5
(e)	$600	2.5%	2
(f)	$10 000	4.5%	3
(g)	$350	7%	18 months
(h)	$12 000	3.5%	30 months

Find the interest earned and the total amount (A = P + I) for each investment. Fluency

	Principal (P)	Rate (R % p.a.)	Time (T)
(a)	$2 000	4%	3 yr
(b)	$5 000	6%	2 yr
(c)	$750	5%	4 yr
(d)	$8 000	3%	5 yr
(e)	$1 200	9%	18 months
(f)	$6 500	4%	2.5 yr

One value is missing from each row. Rearrange the formula to find the unknown. Fluency

	Principal (P)	Rate (R % p.a.)	Time (T years)	Interest (I)	Find
(a)	$3 000	?	3	$360	R = ?
(b)	$5 000	?	2	$450	R = ?
(c)	$4 000	6%	?	$480	T = ?
(d)	$2 000	5%	?	$700	T = ?
(e)	?	7%	4	$560	P = ?
(f)	?	6%	5	$900	P = ?

State whether each statement is True or False. If false, write the correct statement. Fluency
1. Doubling the principal doubles the simple interest earned.
2. Doubling the rate and halving the time leaves the simple interest unchanged.
3. Simple interest means the interest earns interest each year.
4. 18 months should be entered as T = 18 in the formula I = PRT ÷ 100.
5. If P = $2000, R = 5%, T = 3 years, then I = $300 and A = $2300.
6. The total amount A is always greater than the principal P for any loan or investment.
Apply simple interest to solve each real-world problem. Show all working using I = PRT ÷ 100. Understanding
1. Jasmine’s Loan. Jasmine borrows $6 000 at 7% p.a. simple interest for 3 years.
  How much interest does she pay? How much does she repay in total?
2. Aiden’s Term Deposit. A term deposit pays 4.8% p.a. simple interest. Aiden invests $4 500 and needs to earn at least $540 in interest.
  For how many full years must he keep the deposit?
3. Sam’s Investment. Sam invests $P at 5% p.a. for 4 years and receives $800 in interest.
  Find P.
4. Car Loan. A car loan of $15 000 is taken over 4 years at 9% p.a. simple interest.
  1. Find the total interest charged.
  2. Find the total amount repaid.
  3. Find the monthly repayment amount.

Compare the two investment options for each scenario. Complete the table, then state which is better and why. Understanding

Both options use a principal of $5 000.

Scenario	Option A	Option B
1	6% for 2 yr	4.5% for 3 yr
2	8% for 1 yr	5% for 2 yr
3	3% for 5 yr	7% for 2 yr

The table below shows the interest earned each year on a simple interest investment. Fill in the missing values, then answer the questions. Understanding

Investment: $4 000 at 5% p.a. simple interest.

Year	Interest earned this year	Total interest so far	Balance (A)
0	—	$0	$4 000
1
2
3
4
5

What pattern do you notice in the “Interest earned this year” column? Why does this happen with simple interest?
After how many years will the balance first exceed $5 000?

Rearrange the simple interest formula to find the unknown in each problem. Understanding
1. Zara invests $8 000 at 5% p.a. simple interest. Her account balance is now $11 200.
  How many years has she been investing?
2. An investment earned $1 750 simple interest over 5 years. The annual rate was 7% p.a.
  Find the original principal.
3. A $9 000 investment grew to $10 350 over 3 years using simple interest.
  Find the annual interest rate.
4. Raj has $6 000 and wants to save $7 500. He can get 3.6% p.a. simple interest.
  1. How much more money does he need?
  2. How many full years will it take?
Extended real-world problems. Show full working. Problem Solving
1. Savings club. Sophie contributes $200 at the start of each year for 5 years into an account paying 4% p.a. simple interest. Each contribution earns interest for the remaining years of the 5-year period (Year 1 contribution earns interest for 5 years, Year 2 for 4 years, etc.).
  Find the total interest earned on all contributions combined.
2. Which friend earns more? Priya invests $10 000 at 8% p.a. simple interest for 3 years. Marcus invests $10 000 at 6% p.a. simple interest for 5 years.
  Who earns more total interest, and by how much?
3. Personal loan comparison. Lena needs to borrow $12 000. Two lenders offer:
  - Lender X: 6% p.a. simple interest for 4 years
  - Lender Y: 8% p.a. simple interest for 3 years
  1. Calculate the total amount repaid to each lender.
  2. Which lender costs less overall?
  3. Which lender has a higher monthly repayment? Calculate both.

Investigation — How does changing each variable affect simple interest? Problem Solving

Use a base case: P = $1 000, R = 5% p.a., T = 4 years. Base interest = $200.

Complete the table by changing one variable at a time and recalculating the interest.

Change made	P	R	T	New Interest	Change from $200
Base case	$1 000	5%	4	$200	—
Double P	$2 000	5%	4
Halve P	$500	5%	4
Double R	$1 000	10%	4
Halve T	$1 000	5%	2
Double R, halve T	$1 000	10%	2

What happens to simple interest when you double the principal?
What happens when you double the rate AND halve the time? Explain why.
Write a general rule: “Simple interest is proportional to ______, ______, and ______.”

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