Everyday mathematics: money, time, travel, finance

Currency & Conversion

In everyday life you often need to convert between different currencies. The exchange rate tells you how many units of one currency equal one unit of another.

Example: If £1 = €1.15, then £5 = 5 × 1.15 = €5.75.

Remember: Always round to the nearest cent/penny when dealing with money.

Percentages & Discounts

Discounts are often given as a percentage. To find the sale price:

1. Calculate the discount amount: $ \text{discount} = \text{original price} \times \frac{\text{discount\%}}{100} $.
2. Subtract the discount from the original price.

Example: A £120 jacket is on sale for 25 % off.

Discount = £120 × 25/100 = £30. Sale price = £120 – £30 = £90.

Simple Interest

Simple interest is calculated as:

$ \text{Interest} = P \times r \times t $

where $P$ is the principal, $r$ is the annual interest rate (as a decimal), and $t$ is the time in years.

Example: £1,000 at 5 % for 3 years gives $1,000 × 0.05 × 3 = £150$ interest.

Savings & Budgeting

Use a simple budgeting table to track income and expenses.

Category	Amount (£)
Income	1,200
Rent	400
Food	200
Entertainment	100
Net Savings	400

Exam Tip: When converting currencies, always check the exchange rate and remember to round to two decimal places. For interest problems, identify the variables $P$, $r$, and $t$ before plugging them into the formula.

Basic Time Units

1 hour = 60 minutes, 1 minute = 60 seconds.

To add times, convert everything to the same unit, add, then convert back.

Example: 2 h 45 min + 1 h 30 min = (2×60+45)+(1×60+30) = 165+90 = 255 min = 4 h 15 min.

Time Zone Conversion

Time zones are offsets from UTC. For example, London is UTC+0, New York is UTC−5.

To convert 14:00 London time to New York time:

14:00 − 5 h = 09:00.

Speed, Distance & Time

Speed = distance ÷ time. Rearranged:

$ \text{Distance} = \text{Speed} \times \text{Time} $

Example: A car travels at 80 km/h for 2 h.

Distance = 80 × 2 = 160 km.

Time Travel Analogy

Think of time like a river: you can measure how far you travel downstream (distance) by knowing how fast you’re moving (speed) and how long you’ve been in the river (time).

Exam Tip: When solving time problems, write down the formula you’ll use before substituting numbers. Check units carefully – they must match!

Fuel Consumption

Fuel consumption is often given as litres per 100 km.

To find fuel needed for a trip:

1. Calculate total distance.
2. Use the formula: $ \text{Fuel} = \frac{\text{Distance} \times \text{Consumption}}{100} $.

Example: A car consumes 6 L/100 km and travels 250 km.

Fuel = (250 × 6)/100 = 15 L.

Speed & Time for Travel

When planning a trip, you might need to find the travel time.

Formula: $ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $.

Example: Distance = 300 km, Speed = 90 km/h.

Time = 300 ÷ 90 = 3.33 h ≈ 3 h 20 min.

Distance Conversion

1 mile ≈ 1.609 km.

To convert 50 miles to kilometres:

50 × 1.609 = 80.45 km.

Travel Budget Example

Use a simple table to estimate costs.

Item	Cost (£)
Fuel	45
Accommodation	120
Food	60
Total	225

Exam Tip: Always check that your distance, speed, and time units are consistent. If speed is in km/h, distance must be in km and time in hours.

Compound Interest

Compound interest is calculated as:

$ A = P \left(1 + \frac{r}{n}\right)^{nt} $

$P$ = principal, $r$ = annual rate, $n$ = compounding periods per year, $t$ = years.

Example: £500 at 4 % compounded monthly for 2 years.

$ A = 500 \left(1 + \frac{0.04}{12}\right)^{12×2} ≈ £528.32 $.

Loan Repayment

Monthly payment for a loan can be found using:

$ M = P \frac{r(1+r)^n}{(1+r)^n-1} $

$r$ is monthly interest rate, $n$ is total payments.

Example: £10,000 loan at 6 % annual interest, 5 years.

Monthly rate $r = 0.06/12 = 0.005$; $n = 5×12 = 60$.

$ M ≈ 10,000 × \frac{0.005(1+0.005)^{60}}{(1+0.005)^{60}-1} ≈ £193.33 $.

Savings Goal Tracker

Set a monthly savings target and track progress.

Month	Target (£)	Actual (£)
Jan	50	45
Feb	50	55
Average	50	50

Exam Tip: For compound interest, remember to convert the annual rate to the correct period (e.g., monthly). When dealing with loans, identify the monthly rate and total number of payments before applying the formula.