Jack invests $1000 at a certain annual interest rate, and he invests another $2000 at an annual rate that is one-half percent higher.

Question

Jack invests $1000 at a certain annual interest rate, and he invests another $2000 at an annual rate that is one-half percent higher. If he receives a total of $160 interest in 1 year, at what rate is the $1000 invested?

Answer 1

The simple interest formula is as follows:

A = P + Prt = P(1 + rt), where

A = the total Accrued Amount (principal + interest)

P = Principal Amount, or the amount invested

r = Rate of Interest per year in decimal

t = Time Period involved in months or years

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The interest portion of the formula is represented by Prt.

Let's convert the word problem into a formula with both rates:

I = P₁r₁t + P₂r₂t, where

P₁ = the portion Jack invested in the simple interest rate of r₁% per year, $1000

r₁ = the first simple interest rate

P₂ = the portion Jack invested in the simple interest rate of r₂% per year, $2000

r₂ = the second simple interest rate

I = the total interest Jack made on the investments, $160

We also know that r₂ = r₁ + 0.005 and t = 1 year.

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We have 2 equations now. Let's plug in the values

Eqn 1. r₂ = r₁ + 0.005

Eqn 2. 1000r₁ + 2000r₂ = $160

Plug Eqn 1 into Eqn 2 and solve for r₁.

1000r₁ + 2000(r₁ + 0.005) = 160

1000r₁ + 2000r₁ + 10 = 160

3000r₁ + 10 = 160

3000r₁ = 150

r₁ = 0.05 = 5%

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So, Jack invested $1000 at 5% per year.