You can put this solution on YOUR website! First lets consider the interest. Adding 4.25% of $13,000 is the same as multiplying it by 1.0425.
This is because we can write percentages as decimals (by dividing them by 100).
The reason we multiply by 1.0425 and not just 0.0425 is because the extra 1 makes sure that we are adding 4.25% of the total to itself.
So after one year goes by the total amount due will be:
After the second year it will be: (to the nearest cent)
We can continue doing this to find how much will be due after each year!
Don't forget each time we multiply by 1.0425 we need to times it by the amount from the previous year, to make sure that the interest is compounded!
Lets keep going:
Third year:
Fourth year:
We could keep going like this, but that would be a bit boring. Lets put some algebra into the equation!
We want the number of years until the amount we need to pay back is greater than $21,000. We know that the loan started out as $13,000, and each year the amount we need to pay back is the amount from the year before multiplied by 1.0425.
So we can put this into a nice, easy equation:
where n is the number of years.
Then taking logs.
and applying the rules of logs:
Then dividing both sides by log(1.0425) gives
Which gives us n = 11.5 years.
However the interest is added on at the END of the year. So the amount we need to pay back will only become greater than $21,000 after 12 years have passed.
So 12 years is the answer!
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