Paula lent Ned $1200 to help him pay for a mountain bike that he desperately wants. She charged him 8%/a simple interest, payable weekly. Ned paid back the loan plus interest, in equal payments over 20 weeks.
a) How much interest will Ned have to pay? [2 marks]
b) What will be the total amount he will have to pay? [1 mark]
c) What will be his weekly payment for the loan? [1 mark]
To calculate the answers to these questions, we need to understand how simple interest works and how it can be applied to this particular scenario.
a) To determine the amount of interest Ned will have to pay, we can use the simple interest formula:
Interest = Principal (amount borrowed) * Rate * Time
In this case, the principal is $1200, the rate is 8% (expressed as a decimal, which is 0.08), and the time is 20 weeks.
Interest = $1200 * 0.08 * 20
To get the answer, we can calculate this expression.
b) The total amount Ned will have to pay is the sum of the principal (amount borrowed) and the interest.
Total Amount = Principal + Interest
We already know the principal is $1200, and we can use the interest calculated in part (a) to determine the total amount.
Total Amount = $1200 + Interest
c) To find out Ned's weekly payment, we need to divide the total amount by the number of weeks he has to pay back the loan.
Weekly Payment = Total Amount / Number of Weeks
We know the total amount from part (b), and we have been given that Ned will make equal payments over 20 weeks, so we can calculate the weekly payment.
Let's calculate the answers to these questions:
a) Interest = $1200 * 0.08 * 20 = $1920
Therefore, Ned will have to pay $1920 in interest.
b) Total Amount = $1200 + $1920 = $3120
Hence, the total amount Ned will have to pay is $3120.
c) Weekly Payment = $3120 / 20 = $156
Therefore, Ned's weekly payment for the loan will be $156.