Question

you invested $29,000 in two accounts paying 5% and 8% annual interest, respectively. if the total interest earned for the year was $2020, how much was invested at each rate? the amount invested at 5% is $\square. the amount invested at 8% is $\square.

Explanation:

Step1: Define variables

Let $x$ = amount invested at 5%, $29000 - x$ = amount invested at 8%.

Step2: Set up interest equation

Total interest: $0.05x + 0.08(29000 - x) = 2020$

Step3: Expand and simplify equation

$0.05x + 2320 - 0.08x = 2020$
$-0.03x + 2320 = 2020$

Step4: Solve for x

$-0.03x = 2020 - 2320$
$-0.03x = -300$
$x = \frac{-300}{-0.03} = 10000$

Step5: Find 8% investment amount

$29000 - x = 29000 - 10000 = 19000$

Answer:

The amount invested at 5% is $\$10000$.
The amount invested at 8% is $\$19000$.