Math Snap

STEP 1

Assumptions1. The principal loan amount, $$, is $\($\)10,550$
. The interest rate, $r$, is $12.25\%$
3. The time for repayment, $t$, is3 years4. The interest is calculated using the simple interest formula $=Prt$

STEP 2

First, we need to find the interest amount on the loan. We can do this by substituting the given values into the simple interest formula.
$$= Prt$$

STEP 3

Now, plug in the given values for the principal amount, interest rate, and time to calculate the interest.
= \($\)10,550 \times12.25\% \times3

STEP 4

Convert the percentage to a decimal value.
$$12.25\% =0.122$$ = \($\)10,550 \times0.122 \times3

STEP 5

Calculate the interest amount.
= \($\)10,550 \times0.1225 \times3 = \($\)1,228.38Round the interest to the nearest dollar.
= \($\)1,228

STEP 6

Now that we have the interest amount, we can find the total amount that needs to be paid back. This includes both the principal amount and the interest.
$$Total\, amount = Principal\, amount + Interest$$

STEP 7

Plug in the values for the principal amount and the interest to calculate the total amount.
Total\, amount = \($\)10,550 + \($\)1,228

Calculate the total amount that needs to be paid back.
Total\, amount = \($\)10,550 + \($\)1,228 = \($\)11,778Round the total amount to the nearest dollar.
Total\, amount = \($\)11,778The interest paid is $1,228 and the total amount paid is $11,778.