Question

Elisa needs money to repair her home air conditioner so she pawns her bicycle. the pawnbroker loans Elisa $270. Six days later, Elisa gets her bicycle back by paying the pawnbroker $279.00. What annual simple interest rate did the pawnbroker charge Elisa? Assume 360 days in a year.

Answer 1

Simple Interest

The interest generated by an initial amount (principal) P in a time t at a rate t is:

I = P.r.t

Elisa pays $279 to get her bicycle back after 6 days. The loan was agreed for $270, thus the interest paid was I = $279 - $270 = $9

The time is t = 6 days. We must express it in years, thus:

t = 6/360

We'll leave it as it is for later calculations.

Solving for r:

`\begin{gathered} r=(I)/(P\cdot t) \\ \text{Substituting:} \\ r=(9)/(270\cdot((6)/(360))) \\ r=(9\cdot360)/(270\cdot6) \\ r=2 \end{gathered}`

The annual simple interest was r = 2*100 = 200%