Respuesta :
We are to determine the amount that you have pay back after borrowing a principal amount ( P ) for ( t ) number of years which is compounded annualy at rate ( R ).
You borrowed a principal amount of:
[tex]P\text{ = \$100}[/tex]The time duration for which we have borrowed the money for is:
[tex]t\text{ = 3 years}[/tex]The annual interest rate coumpounded each year is:
[tex]R\text{ = 9\% / year}[/tex]Step 1: Determine the simple interest that accumulated at the end of ( t ) years.
The folllowing formula is used to determine the simple interest that the borrower has to pay once the period of borrowing/lending is over i.e ( t ) years.
The simple interest is the proportional rate of interest ( R ) and the initial borrowed/loaned amount called principal amount ( P ).
[tex]\text{Simple Interest ( I ) = }\frac{P\cdot R\cdot t}{100}[/tex]Use the above simple interest formula ( I ) by plugging in the respective values as follows:
[tex]\text{Simple Interest ( I ) = }\frac{100\cdot9\cdot3}{100}\text{ = \$27}[/tex]Therefore, the total amount of interest that the borrower must pay as an extra ( over the borrowed amount ) is $27.
Step 2: Determine the total amount that is to be returned/paid to the lender
The total amoun that is to be paid by the borrower ( you ) to the lender is the principal amount borrowed ( P ) and the amount of interest accumulated for the contractual time period i.e ( I ).
[tex]\begin{gathered} \text{Total amount to be paid = P + I} \\ \text{Total amount to be paid = \$100 + \$27} \\ \text{Total amount to be paid = }127 \end{gathered}[/tex]Therefore, the amount that you need to pay altogether is:
[tex]\textcolor{#FF7968}{127}\text{\textcolor{#FF7968}{ dollars}}[/tex]