Math  /  Numbers & Operations

QuestionThe hire-purchase plan requires a deposit of $135\$ 135 followed by 6 monthly payments of $82.35\$ 82.35 each. (b) Calculate (i) the total amount of monthly payments,
Answer: \ \qquad$ [2] (ii) the total hire-purchase price,
Answer: \ \qquad$ [2] (iii) the amount that can be saved by paying cash.

Studdy Solution

STEP 1

What is this asking? We need to figure out the total cost of a hire-purchase plan, and how much cheaper it would be to just buy it outright for $630\$630. Watch out! Don't forget to add the initial deposit to the total monthly payments to get the *total* hire-purchase price!

STEP 2

1. Calculate Total Monthly Payments
2. Calculate Total Hire-Purchase Price
3. Calculate Savings by Paying Cash

STEP 3

We know there are **6 monthly payments** of $82.35\$82.35 each.
To find the total amount of monthly payments, we **multiply** the number of payments by the amount of each payment.
This is like adding 82.3582.35 to itself six times!

STEP 4

6$82.35=$494.10 6 \cdot \$82.35 = \$494.10 So, the total amount of the monthly payments is $494.10\$\textbf{494.10}.

STEP 5

The **total hire-purchase price** is the sum of the initial **deposit** and the **total monthly payments**.
We've got our total monthly payments from the previous step, and we know the deposit is $135\$\textbf{135}.
Let's add them up!

STEP 6

$135+$494.10=$629.10 \$135 + \$494.10 = \$629.10 Therefore, the total hire-purchase price is $629.10\$\textbf{629.10}.

STEP 7

The problem tells us the cash price is $630\$630.
We just calculated the total hire-purchase price to be $629.10\$\textbf{629.10}.
To find the savings, we **subtract** the hire-purchase price from the cash price.

STEP 8

$630$629.10=$0.90 \$630 - \$629.10 = \$0.90 Wow, paying with the hire-purchase plan saves us $0.90\$\textbf{0.90} compared to paying cash!

STEP 9

(i) Total monthly payments: $494.10\$494.10 (ii) Total hire-purchase price: $629.10\$629.10 (iii) Savings by paying cash: $0.90\$0.90

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