Work each investment problem using simple interest. An...

Work each investment problem using simple interest.
An artist invests in a tax-free bond paying $6 \%,$ and $\$ 6000$ more than three times as much in mutual funds paying $5 \% .$ Her total annual interest income from the investments is S825. How much does she invest at cach rate?

Key Concepts

Simple Interest

Simple interest refers to a method of calculating interest where the interest is directly proportional to the principal, the annual interest rate, and the time period. The formula used is I = P × r × t, meaning that the interest does not compound over time.

Investment Word Problems

Investment word problems involve setting up algebraic equations to represent relationships between different parts of an investment. They require identifying unknown variables, translating the problem's language into mathematical expressions, and using the known interest rates to calculate the total interest earned.

Linear Equations

Linear equations are used to solve for unknown variables in investment scenarios by representing the relationships between the invested amounts and the accrued interests. Formulating and solving these equations helps determine the individual amounts invested at different rates.

Transcript

00:02 All right, we're working with another investment problem.

00:06 And this time we have a bond that gets 6 % interest and a mutual fund that gets 5 % interest.

00:15 And we know that the mutual fund gets $6 ,000 more than three times the amount of money going into the bond.

00:24 We also know that the total interest from these two accounts after one year is $825.

00:30 I'm going to define our variable and base everything off of knowing how much money goes into the bonds.

00:37 So we're going to use b for money invested in.

00:52 You will see i already use that b up here to talk about the mutual fund.

00:57 Okay, to write our equation, we need to think about the fact that we have the 6 % for the bond.

01:04 That's 0 .06 times b, the number of dollars being invested, plus we're putting money into that mutual fund at 5%.

01:15 And that money is found by going 6 ,000 plus 3b, and added together they equal 825.

01:29 We're going to simplify the left side of our equation first by using the distributive property to multiply out this 5 % times the amounts in the parentheses.

01:43 So we have 0 .06b plus 0 .05 times 6 ,000, which is $300.

01:54 And 0 .05 times 3b is 0 .15b.

02:01 And that still equals 825.

02:05 We're going to combine like terms.

02:09 And 0 .15 plus 0 .06 is 0 .21b plus 300 equals 825.

02:23 Now we want to isolate b.

02:25 So we're going to start by subtracting 300 from each side...