Final answer:
By using the formula for simple interest to work backwards, we find that Mr. Lee's original loan amount was approximately $800. This is done by setting up an equation with the amount paid back, the time period of 8 months, and the annual interest rate of 5.4%.
Step-by-step explanation:
To determine how much Mr. Lee's original loan was, we need to use the formula for calculating simple interest which is given as:
I = P × R × T
Where I is the interest paid, P is the principal amount (initial loan), R is the annual interest rate, and T is the time in years.
In this case, we are looking for the principal P and we have:
- Total amount paid back after 8 months: $840.84
- Annual interest rate: 5.4%
- Time: 8 months or ⅓ years
We assume the interest is simple and not compounded. First, we convert the interest rate into decimal form: 5.4% = 0.054. Then convert the time into years: 8 months = ⅓ years.
The total amount paid back (A) is the principal plus the interest earned:
A = P + (P × R × T)
Now we can solve for P:
$840.84 = P + (P × 0.054 × ⅓)
By isolating P, we find:
P ≈ $800
Therefore, the original loan amount was $800.