Solve each problem. See Example 4. In planning her retirement,...

Question

Solve each problem. See Example 4. In planning her retirement, Kaya deposits some money at 2.5% interest, and twice as much money at 3%. Find the amount deposited at each rate if the total annual interest income is $850.

Accepted Answer

Hello, today we're going to be solving the following word problem. So the word problem states that Bruce invest some money in a fixed deposit at a 7% interest rate. And he lends his friend four times the amount of money at 18% interest. If the total annual interest income is $316, we want to find the amount of money invested in each rate. So we are told that Bruce makes a deposit at two interest rates, one at 7% and the other at 18% for the 7% interest rate. We don't know how much money he invested in this scenario. So we're going to let x represent the amount of money that was deposited into that account. And in the 18% scenario, we are told that he lends his friend four times the amount of money compared to what he deposited at the 7% interest rate. So that means that he lent his friend four times the unknown amount of money which we can represent. As for X. Now, what we wanna do is we want to come up with an equation that can help us solve for the unknown amount of money. And we are told that the annual interest income is going to be $316. So in order to solve for X, we can go ahead and come up with an equation where we take the amount of money deposited in the account at 7% interest And added with the money made at four times the deposit times the 18% interest rate. And that is going to equal to $316 because that's going to be the annual interest income. So now what we want to do is simplify this equation in order to solve for X. So we want to go ahead and convert 7% and 18% into a decimal. And in order to do that, we're going to divide both of the percentages by 100, dividing the percentages by 100 is going to give us X times 0.7 plus four, X times 0.18 is going equal to 316. On the left hand side, X times 0.7 is going to give us 0. X and four X times 0.18 is going to give us 0.72 X. Now we can go ahead and add the left hand side together and 0. X plus 0.72 X is going to give us 0.79 X. And finally, in order to solve for X, we're going to divide both sides of this equation by 0.79. And doing this is going to leave us with the final X amount of 400. So that means we've figured out the unknown value for the amount of money deposited at each rate. Now, we can go ahead and replace every X in both of the scenarios with this amount. So if we do this for the 7% interest rate, that means he had to deposit $ And for the 18% interest rate. Keep in mind that he gave his friend four times the amount of money. So that's going to be four times 400 which is going to equal to $1,600. So with that being said, For the 7% interest rate, he deposited $400 and at the 18% interest rate, he gave his friend $1600. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Solve each problem. See Example 4. In planning her retirement, Kaya deposits some money at 2.5% interest, and twice as much money at 3%. Find the amount deposited at each rate if the total annual interest income is \$850.

Key Concepts

Simple Interest Calculation

Setting Up Algebraic Equations

Solving Systems of Linear Equations

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