Question

A trust fund worth $25,000 is invested in two different portfolios. This year, one portfolio is expected to earn 5.25% interest and the other is expected to earn 4%. Plans are for the total interest on the fund to be $1,150 in one year. How much money should be invested at each rate?

Answer 1

$12 000 in Portfolio 1 and $13 000 in Portfolio 2

Explanation:

The formula for simple interest is

I = Prt

For each portfolio, t = 1 yr

For Portfolio 1, i = 5.25 % = 0.0525

For Portfolio 2, i = 4 % = 0.04

Let x = amount invested in Portfolio 1. Then

25 000 - x = amount invested in Portfolio 2 and

`\begin{array}{rcr}0.0525x + 0.04(25000- x) & = & 1150\\0.0525x+ 1000 - 0.04x & = & 1150\\0.0125x + 1000 & = & 1150\\0.0125x & = & 150\\x & = & 12000\\\end{array}`

25 000 - x = 25 000 - 12 000 = 13 000

So, $12 000 is invested in Portfolio 1 and $13 000 is invested in Portfolio 2.

Check:

`\begin{array}{rcl}0.0525 * 12000 + 0.04(25000 - 12000)& = & 1150\\630 + 0.04(13000) & = & 1150\\630 + 520 & = & 1150\\1150 & = & 1150\\\end{array}`

OK.