College algebra

Question

You have $10,000 that you invested in two mutual funds last year. The first fund, the International Fund, paid the equivalent of 5.2% simple interest. The second fund, the Real Estate fund, paid 2.1% simple interest. If the total earned in that year was $430.10, how much did you invest in each account. Find the solution using only one variable

Answer 1

Hello, thank you for taking the time to post your question!

The key on solving this type of question is to set up an algebraic expression that represents the underlying data. On this one we have

(International Fund Amount x 0.052) + (Real Estate Fund Amount x 0.021) = Total

0.052x + 0.021(10000 – x) = 430.10

0.052x – 0.021x + 210 = 430.10

0.031x = 220.10

x = 220.10 / 0.031 = 7100

meaning that the other account had 10000 – 7100 = 2900

so the amount invested in the Real Estate Fund is $2900 and the amount invested in the International Fund is $7100

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Let x be the amount invested in the International Fund. Then, 10000-x is the amount invested in the Real Estate Fund.

 

The interest earned on each fund it found using the formula I = Prt, where P is the principal, i the interest rate expressed as a decimal, and t the time in years.

 

The sum of the interest earned on both accounts adds up to $430.10, so you can set up an equation,

 

.052x + .021(10000 - x) = 430.10 .

 

To solve this, distribute over the parentheses, collect like terms, clear the decimals by multiplying by 1000, then use algebra to finish:

 

.052x + 210 - .021x = 430.10

 

.031x = 220.10

 

31x = 220100

 

x = 220100/31 = 7100.

 

This means that $7100 was invested at 5.2% and $2900 invested at 2.1%.