College Algebra: Word Problems/Money

Question

A bank invested ​$450,000 last year in mutual funds. The conservative fund earned 9​% simple interest. The growth fund earned 14​% simple interest. At the end of the​ year, the bank had earned ​$48000 from these mutual funds. How much did it invest in each​ fund?

Answer 1

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

The key on this type of question is finding a way to relate the variables to one another in an algebraic expression. On this one we have

x + y = 10000         because we know that the bank invested $450000 in total between the two assets

0.09x + 0.14y = 48000     because between the 9% conservative return and 14% growth return the bank earned $48000 in total interest

I would substitute in the first expression into the second and then solve for the underlying value of “y” … when I do that I get y = 150000, meaning that x = 450000 – 150000 = 300000

So the bank invested $300,000 at the 9% rate and then the remaining $150,000 at the 14% rate

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

x = amount of money invested in conservative funds

y = amount of money invested in growth funds

x + y = 450,000

Simple interest formula:

A = P*(1 + rt),

where P is the principal (initial amount), r is the interest rate, t is the time in years, and A is the final amount.

Final amount of conservative funds after 1 year (t=1):

x * (1 + 0.09)

Final amount of growth funds after 1 year (t=1):

y * (1 + 0.14)

Total amount of both funds after 1 year:

x*(1+0.09) + y*(1+0.14) = 450,000 + 48,000

1.09x + 1.14y = 498,000 (Equation 1)

We know that x+y = 450,000

This means that x = 450,000 - y

If we plug in this expression for x into Equation 1, we get:

1.09(450,000 - y) + 1.14y = 498,000

490,500 - 1.09y + 1.14y = 498,000

0.05y = 7500

y = 150,000

x = 450,000 - y = 300,000

The bank invested $300,000 in conservative funds and $150,000 in growth funds.