Your brother lends you $125 at an annual interest rate of 25%. If you want to pay no more than $62.50 in simple interest, in how many years will you need to pay off the loan? Use the formula: I = Prt.
The Correct Answer and Explanation is :
To determine how many years it will take to pay off a loan of $125 at an annual interest rate of 25% with a maximum allowable simple interest of $62.50, we can use the formula for simple interest:
[
I = Prt
]
Where:
- (I) = interest
- (P) = principal (the initial amount of money borrowed)
- (r) = annual interest rate (as a decimal)
- (t) = time in years
In this case:
- (I = 62.50)
- (P = 125)
- (r = 25\% = 0.25)
We want to find (t), the time in years. We can rearrange the formula to solve for (t):
[
t = \frac{I}{Pr}
]
Now, we can substitute the values into the equation:
[
t = \frac{62.50}{125 \times 0.25}
]
Calculating the denominator:
[
125 \times 0.25 = 31.25
]
Now we can substitute back into the formula for (t):
[
t = \frac{62.50}{31.25}
]
Calculating (t):
[
t = 2
]
Thus, it will take 2 years to pay off the loan while keeping the interest paid to no more than $62.50.
Explanation
The formula for simple interest, (I = Prt), is foundational in understanding loans and investments. In this scenario, you have borrowed $125 from your brother, and you’re willing to pay up to $62.50 in interest, which is half of your principal.
By rearranging the formula, we derived a clear method to find the time required to accumulate that interest. It highlights the relationship between the principal amount, the interest rate, and the duration of the loan. Given the high interest rate of 25%, it’s essential to keep the interest within a manageable limit to avoid excessive debt.
Thus, by solving the equation, we found that it would take you 2 years to pay off the loan under these conditions, ensuring the interest remains at or below your specified limit. This understanding is crucial for financial planning and maintaining good relationships, especially when borrowing from friends or family.