Question

Someone help me please. I'm trying so hard to understand this.

A bank account has a beginning balance of
$560.00. After 6 months, the balance in the account has increased to $572.60. What interest rate is being earned annually on this account?

.045%
2.20%
2.25%
4.5%

Answer 1

How much interest was earned in the 6 months?
I'm not talking about the interest rate, I mean, how much money in dollars was earned in interest in the 6 months?

Answer 2

$12.60?

Answer 3

Yes, exactly.
It's the difference between the amount of money before and after the 6 months passed.
$572.60 - $560 = $12.60

Answer 4

$12.60 in interest was earned in 6 months.
At the same rate, how much would be earned in 1 year.

Answer 5

Ohhh, I see now.

Answer 6

But wait, I need to find the percentage...

Answer 7

One step at a time.
What is the total interest that would be earned in 1 year at this rate?

Answer 8

Are you still there?

Answer 9

I'm here.. I'm confused.

Answer 10

No need for confusion.
Let's make it clear.
In 6 months, $12.60 in interest was earned.
1 year is 2 times 6 months, so in 1 year, two times that interest would be earned.
What is 2 * $12.60 = ?

Answer 11

25.2

Answer 12

Correct.
Now there is only one step left.
We need to find out what percentage 25.20 is of 560.

Answer 13

4.5%?

Answer 14

We can do that with a proportion:

560 is to 100% as 25.20 is to x%

\(\dfrac{560}{100} = \dfrac{25.20}{x}\)

Answer 15

We cross multiply:

\(560x = 25.20 \times 100\)

\(560x = 2520\)

\(x = \dfrac{2520}{560} \)

\(x = 4.5\)

Answer: 4.5%

Answer 16

You are correct.

Answer 17

The reason that our second step was to multiply $12.60 by 2 is that the $12.60 in interest if for 6 months. The question is asking what the annual interest rate is, so we needed to know how much interest would be earned in 1 year.

Answer 18

Good job!
Bye