Problem

See Example 3. Swimming. In $1930,$ a man swam do…

01:27

Problem 20 Medium Difficulty

See Example 2.
Banking. Three years after opening an account that paid simple interest of $6.45 \%$ annually, a depositor withdrew the 3,483 dollars in interest earned. How much money was left in the account?

Answer

$$\$ 2,918.31$$

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Precalculus

Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 4

Formulas

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Video Transcript

in this problem, we were told. Three years after opening an account that paid simple interests of 6.45% a depositor withdrew the $3483 in interest earned. We want to determine how much money was left in the account. Well, because we talk about simple interests, we're going to need to use the equation. I equals P R T where I stands for the amount of interest earned which we're told was $3483. So that will be our I. Now the principal is what we initially deposited, but not sure of yet. We were told the rate was 6.45%. But remember, we need to make this percent into a decibel, so we'll move our decimal 0.2 places to the left. So what we know is that our our will be 0.645 and t stands for time, which in this case, we were told three years now what's happening is in this problem is they said that this person is going to withdraw all of the interest earned. Well, that will mean that they're gonna be left with what they initially started with, which is just our principal. So essentially, what we're looking for in this case is just the value of our principal. So what I'm going to do first is solved My original formula for Pete Well, he currently is getting multiplied by our times t So don't do that. I'm going to divide both sides by r times t so we will be left with I divided by our times. T is equal to P because both the art and the teas will cancel each other up. Now, I simply need to substitute my values into my formula. Well, we said I was $3483 the re was 0.645 and that Artie was equal to three. And now we simply just need to solve this formula. So what we're going to do first is multiply 0.645 times three, which gives us 30.1935 So I'm gonna go over here to the right, so we're gonna have 3483 divided by 0.1935 and that will equal to P. So now what we need to do is divide 3483 by 34830.1935 and that will give us our principle. And what we find is that will equal to $18,000 So that's how much will be left in the account.

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