Question

You are given the total annual interest earned from a total of $8,000 invested in two funds paying the given rates of simple interest. Write and solve a system of equations to find the amount invested at each rate.

Annual Interest $290
Rate 1 3%
Rate 2 4%

Answer 1

The amount invested in each fund is

At rate 1, 3% amount invested = $3,000

At rate 2, 4% amount invested = $5,000

Explanation:

Here we have

Interest, I = Principal, P × Rate, R

Therefore, we have for the first rate of 13% (13% = 0.13)

I₁ = P₁ × 0.03

For the second rate of 24% we have

I₂ = P₂ × 0.04

We are told that

I₁ + I₂ = $290

Therefore,

P₁ × 0.03 + P₂ × 0.04 = $290......................(1)

Also

P₁ + P₂ = $8,000............................................(2)

Solving the two equations, we have

Where P₂ = $8,000 - P₁

Substituting in equation (1) we get,

P₁ × 0.03 + ($8,000 - P₁) × 0.04 = $290

$320 - 0.04·P₁ + 0.03·P₁ = $290

-0.01·P₁ = $290 - $320 = -$30

P₁ = $3000 and therefore,

P₂ = $8,000 - P₁ = $8,000 - $3000 = $5,000.