Of course! Let's break this problem down into parts and solve it step-by-step.
Given:
- Principal amount borrowed by Mrs. Collins: [tex]\( \$12,000.00 \)[/tex]
- Annual interest rate: [tex]\( 8\% \)[/tex] (which can be written as [tex]\( 0.08 \)[/tex] in decimal form)
- Time period: [tex]\( 3 \)[/tex] years
Part (a): Calculate the interest Mrs. Collins has to pay
To find the interest, we use the formula for simple interest:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Substituting the given values:
[tex]\[ \text{Interest} = 12,000 \times 0.08 \times 3 \][/tex]
This calculation yields:
[tex]\[ \text{Interest} = \$2,880.00 \][/tex]
So, Mrs. Collins would have to pay an interest of [tex]\( \$2,880.00 \)[/tex].
Part (b): Calculate the total amount Mrs. Collins has to repay
To find the total amount that Mrs. Collins has to repay, we add the interest to the principal amount:
[tex]\[ \text{Total Repayment} = \text{Principal} + \text{Interest} \][/tex]
Substituting the given values and the calculated interest:
[tex]\[ \text{Total Repayment} = 12,000 + 2,880 \][/tex]
This calculation yields:
[tex]\[ \text{Total Repayment} = \$14,880.00 \][/tex]
So, the total amount Mrs. Collins has to repay is [tex]\( \$14,880.00 \)[/tex].
