Hamid borrowed a sum of money for 3 years at an interest rate of 3.5% per annum simple interest to pay for his car. If the total interest Hamid paid on the loan was $10 374, find the sum of money that he borrowed. Answer $ ... The table shows information collected by Hamid about his driving in 2023.

Description	Value
Total distance driven in 2023	16 992 km
Average price paid for petrol	$2.72 per litre
Average petrol consumption of his car	6.7 litres per 100 km

Calculate the total amount Hamid paid for petrol in 2023. Answer $ ... At the start of 2020, Hamid bought his car at a cash price of $120 500. Each year the value of the car decreases by 5% of its value at the start of the year. At the end of 2023, Hamid decided to sell his car. Explain why the percentage reduction at the end of three years is not 15% of $120 500. Calculate the value of his car at the end of 2023. Give your answer correct to the nearest dollar. Answer $ ...

1. Write the simple interest equation using the given rate and time.

Simple interest:
$I=Prt$
Given $I=10374$, $r=3.5\%=0.035$ and $t=3$,
$10374=P(0.035)(3)$

2. Solve for the sum borrowed.

$P=\frac{10374}{0.035\times 3}$
$P=98800$

1. Calculate the total amount of petrol used in litres.

Petrol used
$= \frac{16\,992}{100}\times 6.7$
$= 1138.464\text{ litres}$

2. Multiply the litres used by the price per litre.

Total cost
$=1138.464\times 2.72$
$=3099.82208$
To the nearest cent, this is $\char36{}3099.82$.

1. State why the three yearly percentage decreases cannot be added as 15% of the original price.

Each year, the car loses $5\%$ of its value at the start of that year. After the first year, the value is already less than $120 500, so the next $5\%$ is calculated on a smaller amount, not on $120 500.

1. Identify the multiplier for a 5% yearly decrease and the number of years of depreciation.

A decrease of $5\%$ means the car keeps
$100\%-5\%=95\%=0.95$
of its value each year.

From the start of 2020 to the end of 2023, there are $4$ yearly decreases.

2. Apply the repeated percentage decrease to the original car price.

Value at the end of 2023
$=120500(0.95)^4$
$=98119.25625$

3. Round the value to the nearest dollar.

$98119.25625\approx 98119$
correct to the nearest dollar.