Substituting into formulas

Substitute given values into linear and non-linear formulas to evaluate the subject, expressing results to appropriate precision with correct units.

Worked examples

Simple interest using I = Prn

Straightforward

Problem

Find the simple interest earned when

P = \$5000

r = 0.06

and

n = 3

using the formula

I = Prn

Compound interest with n = 2

Moderate

Problem

Find

A

using

A = P(1+r)^n

when

P = \$8000

r = 0.04

and

n = 2

. Give your answer to the nearest cent.

Reducing balance depreciation

Challenging

Problem

A car is purchased for

C = \$24\,000

and depreciates at

r = 0.20

per year. Use

V = C(1-r)^n

to find its value after

n = 3

years. Interpret the result.

Practise

Q1·Straightforward

The compound interest formula is

A = P(1+r)^n

. Find

A

when

P = 6000

r = 0.04

and

n = 1

Q2·Straightforward

Use the simple interest formula

I = Prn

to find

I

when

P = 3500

r = 0.05

and

n = 4

Q3·Straightforward

The body mass index formula is

\text{BMI} = \dfrac{m}{h^2}

, where

m

is mass in kilograms and

h

is height in metres. Find the BMI of a person with mass

81\,\text{kg}

and height

1.8\,\text{m}

. Give your answer to two decimal places.

Q4·Straightforward

Use the temperature conversion formula

F = 1.8C + 32

to find the temperature in degrees Fahrenheit when

C = 35

Q5·Moderate

Find

A

using

A = P(1+r)^n

when

P = \$2000

r = 0.05

and

n = 3

. Give your answer to the nearest cent.

Q6·Moderate

The volume of a cylinder is given by

V = \pi r^2 h

. Find the volume when

r = 5\,\text{cm}

and

h = 6\,\text{cm}

. Give your answer to two decimal places.

Q7·Moderate

The body surface area (BSA) is approximated by

\text{BSA} = \sqrt{\dfrac{h \times w}{3600}}

where

h

is height in centimetres and

w

is weight in kilograms. Find the BSA of a person with height

165\,\text{cm}

and weight

60\,\text{kg}

. Give your answer in square metres to two decimal places.

Q8·Moderate

A car of mass

m = 1500\,\text{kg}

is moving at

v = 20\,\text{m/s}

. Use the formula

E = \dfrac{1}{2}mv^2

to find its kinetic energy in joules.

Q9·Challenging

An investment of

\$5000

earns compound interest at

6\%

per year. Use

A = P(1+r)^n

with

P = 5000

r = 0.06

and

n = 4

to find the value of the investment after 4 years. Give your answer to the nearest cent.

Q10·Challenging

A ball is thrown upward from a height of

2\,\text{m}

above the ground. Its height in metres after

t

seconds is given by

h = -4.9t^2 + 14.7t + 2

. Find the height of the ball after

2

seconds.

Q11·Challenging

A machine is purchased for

\$18\,000

and loses value at a rate of

15\%

per year. Use the reducing balance formula

V = C(1-r)^n

with

C = 18\,000

r = 0.15

and

n = 4

to find the value of the machine after 4 years. Give your answer to the nearest dollar.

Q12·Challenging

A circular swimming pool has outer radius

R = 10\,\text{m}

. A path of uniform width surrounds it; the path has inner radius

r = 7\,\text{m}

. Use

A = \pi(R^2 - r^2)

to find the area of the path. Give your answer to two decimal places.