Liam borrowed a sum of money from his parents as an interest free loan to help him pay college. We know that 6 months into the loan,owned 17,900 and that 15 months into into the loan he owned 14,750.
1. What is the original amount?
2. How long will it take to pay back?
Please help i'm having trouble with this 2 questions
how to change improper fraction 31/6 to a mix nember or a whole number
To solve this problem, we can set up a system of equations using the given information.
Let's denote the original amount as "P" and the time it takes to pay back the loan as "t" in months.
1. To find the original amount, we can set up the following equation:
P + (0.00)(P) = 17,900
Since it is an interest-free loan, there is no interest accrued on the borrowed amount.
Simplifying the equation, we get:
1.00P = 17,900
P = 17,900
Therefore, the original amount borrowed was $17,900.
2. To find the time it takes to pay back the loan, we can set up another equation:
P + (0.00)(P) = 14,750
Again, since there is no interest, there is no change in the borrowed amount over time.
Simplifying the equation, we get:
1.00P = 14,750
P = 14,750
This equation tells us that the remaining amount owed after 15 months is $14,750.
Now, we can subtract the remaining amount from the original amount to find how much has been paid off:
17,900 - 14,750 = 3,150
This tells us that $3,150 has been paid off in the first 15 months.
Next, we can set up another equation based on the time it has taken to pay off this amount:
3,150 / t = 14,750
Solving for t, we get:
t = 14,750 / 3,150
t ≈ 4.68 months
This means that it will take approximately 4.68 months to pay back the loan completely.
In summary:
1. The original amount borrowed was $17,900.
2. It will take approximately 4.68 months to pay back the loan completely.