A student takes out two loans to help pay for college expenses. The total amount of money borrowed is $8050. Both loans have interest that accrues annually. The first loan has an interest rate of 8.5%, and the second loan has an interest rate of 2.5%. After the first year, the interest from both loans total $297.25. Find the initial amount borrowed at 2.5%. Round to the nearest dollar.

Question

A student takes out two loans to help pay for college expenses. The total amount of money borrowed is $8050. Both loans have interest that accrues annually. The first loan has an interest rate of 8.5%, and the second loan has an interest rate of 2.5%. After the first year, the interest from both loans total $297.25. Find the initial amount borrowed at 2.5%. Round to the nearest dollar.

Amount at 2.5%:
can you please check my answer..thanks
is it
$ 6.450.00

Answer 1

If $x at 2.5%, then

0.025x + 0.085(8050-x) = 297.25
so your answer looks good

Answer 2

amount borrowed at 8.5% --- x

amount borrowed at 2.5% ---- 8050-x

.085x + .025(8050-x) = 297.25
times 1000
85x + 25(8050-x) = 297250
85x + 201250 - 25x = 297250
60x = 96000
x = 1600

amount borrowed at 8.5% = $1600
amount borrowed at 2.5% = 8050 - 1600 = 6450

Answer 3

To find the initial amount borrowed at 2.5%, we'll need to set up an equation based on the given information.

Let's assume the initial amount borrowed at 8.5% interest is x (in dollars). Therefore, the initial amount borrowed at 2.5% interest will be $8050 - x (since the total borrowed is $8050).

The interest accrued in one year on the first loan at 8.5% interest can be calculated by multiplying the initial amount borrowed by the interest rate (8.5% is equivalent to 0.085):

Interest from first loan = x * 0.085

The interest accrued in one year on the second loan at 2.5% interest can also be calculated by multiplying the initial amount borrowed at 2.5% interest by the interest rate (2.5% is equivalent to 0.025):

Interest from second loan = ($8050 - x) * 0.025

According to the given information, the total interest accrued in one year from both loans is $297.25:

Interest from first loan + Interest from second loan = $297.25

Substituting the previously calculated values:

x * 0.085 + ($8050 - x) * 0.025 = $297.25

To solve for x, we can simplify and solve the equation:

0.085x + 201.25 - 0.025x = 297.25

Combine like terms:

0.06x + 201.25 = 297.25

Subtract 201.25 from both sides:

0.06x = 96

Divide both sides by 0.06:

x = 1600

Therefore, the initial amount borrowed at 2.5% is $8050 - $1600 = $6450.

So, the correct answer is $6450.