A bank loaned out $26,000 to a customer, some it at a 5% annual rate, and the rest 12%. the total interest received after one year was $1902. Find the amount loaned at 5%

Question

I dont know what to do or how to get started...Please help!

Answer 1

if the amount loaned by 5% is x, the amount loaned by 12% is (26,000 -x)

when we calculate the first year's interest,

1,902 = x * 5% + (26,000 - x) * 12%

1,902 = 0.05x + 260 * 12 - 0.12x

0.07x = 3,120 - 1,902 = 1218

x = 1218 * 100 / 7

x = $17,400

Answer 2

They way I would go about setting up this problem is to write out everything we know and expressions for what we want to know, using the compound interest formula A = P(1 + (r/n))^nt. We know that the total amount has to be 26000 + 1902, so we can set A to 27902.

Then we would want to write an expression for how much was made at the 5% rate. Since the rate is annual, n = 1 and r = .05, with a t that we want to solve. From this we can write A_.05 = 26000(1 + .05)^t.

The rest of the money is made at a 12% rate, and since the t in the formula is in terms of years, we can simply have t be 1 – t, since they have to add up to be a year. The tricky part here is figuring out the principle amount for this part. If we think it through, though, we see that the principle amount would have to be the money made from the 5% portion of it: we then see that A_.12 = A_.05(1 + .12)^1–t.

With this, we can write out the whole equation to solve:

A_total = A_.05 + A_.12

27902 = 26000(1.05)^t + 26000(1.05)^t(1.12)^1–t

Simplifying, we can write

27902 = 26000(1.05)^t(1 + 1.12^1–t).

With this, you can start solving for t using properties of exponents and logarithms. Once you do, though, remember what the original question asked!

I hope this helped. Let me know if you have any questions!

Answer 3

The total interest was $1902, and the standard interest equation is

I = Pr where I is the total interest, P is the principal amount, and r is the rate of interest.

You are provided with all the necessary information to build your equation. Note that you will have two different "Pr" values because there are two different interest rates principal amounts. You know that the second principal amount would just be 26000 minus whatever the first one is.

The equation you can construct is 1902 = P(.05) + (26000-P)(.12).

Solve for P and you can find the amounts loaned at each rate.