Year 10AC9M10A04

Simple Interest and Hire Purchase

Use mathematical modelling to solve applied problems involving growth and decay, including financial contexts; formulate problems, choosing to apply linear, quadratic or exponential models; evaluate and modify models and report assumptions, methods and findings.

Things you should know.

Method

Simple interest

A = P(1 + in)

$A$ = final amount, $P$ = principal, $i$ = interest rate as a decimal, $n$ = number of years.

Hire purchase

A = P(1 + in)

Same formula. Hire purchase is simple interest.

Compound interest

A = P(1 + i)^{n}

Interest earns interest.

Inflation

A = P(1 + i)^{n}

Same formula as compound interest.

Worked example

e.g.

\text{a device sold for } \$3\,000 \text{ cash is bought on hire purchase at } 12\% \text{ p.a. over 3 years}

Write down list of information $P = 3000,\quad i = 0.12,\quad n = 3$
Find a formula $A = P(1 + in)$
Substitute $A = 3000(1 + 0.12 \times 3)$
Solve $A = \$4\,080$

Practice

Complete the following using the simple interest formula:

P = \$1\,500,\ i = 12\%,\ n = 2 \text{ years. Find } A

Answer

A = \$1\,860

A = \$600,\ i = 5\%,\ n = 4 \text{ years. Find } P

Answer

P = \$500

P = \$400\,000 \text{ at } 5\% \text{ for } 8 \text{ years. Find } A

Answer

A = \$560\,000

P = \$200\,000,\ i = 15\%,\ n = 5 \text{ years. Find } A

Answer

A = \$350\,000

P = \$500,\ A = \$1\,500,\ n = 10 \text{ years. Find } i

Answer

i = 20\%

P = \$2\,000,\ i = 8\%,\ n = 5 \text{ years. Find } A

Answer

A = \$2\,800

A \text{ car costs } \$18\,000 \text{ cash, or hire purchase at } 9\% \text{ p.a. over 4 years. Find the total paid}

Answer

A = \$24\,480

P = \$1\,000,\ A = \$1\,450,\ i = 9\%. \text{ Find } n

Answer

n = 5 \text{ years}