Question

Lucy wants to but a new car but needs money for the down payment. Her parents agree to lend her money at an annual rate of 5%, charged as simple interest. They lend her $4000 for 2 years. She makes no payments except the one at the end of that time.

Answer the following questions:
How much total interest will Lucy have to pay?
What will the total repayment amount be (including interest)

Answer 1

To calculate the total interest that Lucy will have to pay, we need to use the formula for simple interest: I = P * R * T, where I is the interest, P is the principal (the amount borrowed), R is the interest rate (as a decimal), and T is the time in years. Using this formula, we can calculate the total interest that Lucy will have to pay as follows:

I = P * R * T

I = $4000 * 0.05 * 2

I = $400

Therefore, the total interest that Lucy will have to pay is $400.

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To calculate the total repayment amount (including interest), we need to add the total interest to the original amount borrowed, which in this case is $4000. Therefore, the total repayment amount will be $4000 + $400 = $4400. This is the amount that Lucy will have to pay back to her parents at the end of the two-year period.

Explanation:

Answer 2

Total interest = $400

Total repayment (including interest) = $4,400

Explanation:

Simple Interest Formula

`\large\boxed{ \sf I = Prt}`

where:

• I = Total interest.
• P = Principal amount.
• r = Interest rate (in decimal form).
• t = Time (in years).

Given:

• P = $4,000
• r = 5% = 0.05
• t = 2 years

To find the total interest, substitute the given values into the formula and solve for I:

`\implies \sf I=4000 \cdot 0.05 \cdot 2`

`\implies \sf I=200 \cdot 2`

`\implies \sf I=400`

Therefore, the total interest Lucy has to pay is $400.

The total repayment amount is the sum of the principal and the interest:

`\implies \sf A=P+I`

`\implies \sf A=4000 +400`

`\implies \sf A=4400`

Therefore, the total repayment (including interest) is $4,400.