You invested $20,000 in two accounts paying 1.45% and 1.59% annua...

Question

You invested $20,000 in two accounts paying 1.45% and 1.59% annual interest. If the total interest earned for the year was $307.50, how much was invested at each rate?

Accepted Answer

Welcome back. I'm so glad you're here. Denise invested $35,000 into two banks. Nice job Denise in that first bank. They gave her 1.35% annual interest rate in the second bank, gave her a 1.52% annual interest rate. And we're also told that the interest total in one year earned at both banks together was $504.50. We are to find, how much did she invest in the first bank. And how much did she invest in the second bank. So what I'm going to do is assign variables to what we're trying to find. We're trying to find how much she put in the first bank. So that's going to be B sub one. We're trying to find out how much she put in the second bank that's going to be B sub two. And we know that when we add B. Sub one Plus b. sub two that equals a total of $35,000. So this is the first of our equations, the first math sentence were writing. And now let's see if we can write another math sentence based on the other information that we've got here. Well we know the total interest earned in the whole year was $504.50. And how do you find what the interest is? Well you're going to take the amount of money you put into the bank and multiply that by the annual interest rate. And so we take the amount she invested in the first bank. Well we don't know what that is, that's B sub one. And we're going to multiply it by its interest rate. I want to note real quick The interest rate. The first bank is 1.35%. We can rewrite that as a decimal 0.0135. And that's what I'm going to use here. The decimal point. And in the second bank she's got 1.52%. Again, we're going to put that as a decimal for this. 0.152. And now I'll write those here. So we take the interest rate at the first bank 0.135. And multiply that by the amount she put into the first bank or B sub one, add that to the interest rate for the second bank. 0.152 times the amount of money she put into the second bank, which is B sub two. Now we've got two sentences, they each have two variables. But we want to sell for one variable at a time. And to do that, we're going to isolate a variable and it's easiest to do it in the first sentence. You can actually go about solving this in different ways, plugging different things in. So you might solve this slightly differently than what you're going to see me demonstrate here. But I am going to take B sub two and subtract it from both sides of the equation. So that on the left hand side, all I've got is B sub one equals. And then on the left hand side I have 35, minus B. Sub two. And what I like about this formula and now we have B sub one by itself. And it's equal to 35,000 minus B. Sub two. And I can take 35,000 minus B. Sub two and plug it in for this B sub one because they're equivalent. Now we can rewrite sentence to our equation number 2504.50 equals 0.135 and no longer A times B sub one. But now times parentheses, 35,000 minus B sub two. And parentheses plus Bring down that other B sub two value 0.152. B sub two. Great. Now we've just got B sub two variables here. We can combine like terms and solve for B sub two. Before we can combine those beasts. Obtuse though, we've got to get the one out of the parentheses. So we'll distribute this 0.135 number. Bring down our 504.50 equals. Now our new number here when we multiply 0.135 times 35,000 that equals $472. minus 0.135 B sub two plus. Bring down our other 10.152. B. Sub two. Now we can bring this $472. over to the left hand side. And we can combine like terms with these b. sub two variables. The left hand side is now a really nice number. It's just 32 equals. And then we combine our B. Sub two variables to get 0. B. C. Two's. We can divide both sides by 0.0017. And now we have b. sub two equals $18,823. awesome. We solved for B. Sub two and now we can go ahead back to this first equation and plug that in for our B. Sub two. And let's figure out what B. Sub one equals. I'll write that a little bit off to the side here. So be sub one equals 35, minus $18,823.53. We subtract those two numbers and B. Sub one equals $16,176.47. Well done and well done Denise. We look at our answer choices and this matches with answer choice. C. We'll catch you on the next one

You invested $20,000 in two accounts paying 1.45% and 1.59% annual interest. If the total interest earned for the year was $307.50, how much was invested at each rate?

Key Concepts

Systems of Equations

Interest Calculation

Variable Representation

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