Questionstion 10 Multiple Choice much will be worth after compound interest is \2.09 \%$ 1W \$1202.09
Studdy Solution
STEP 1
What is this asking? If we put in the bank, and the bank gives us interest every year, compounding annually, how much money will we have after years? Watch out! Don't forget that "compounding annually" means the interest earned in the first year also earns interest in the second year!
STEP 2
1. Calculate the value after the first year.
2. Calculate the value after the second year.
STEP 3
Alright, let's **kick things off**!
We start with our **initial investment** of .
STEP 4
Now, we need to figure out the **interest earned** in the first year.
The **interest rate** is , which, as a decimal, is .
To find the interest earned, we **multiply** the **initial investment** by the **interest rate**:
STEP 5
So, after one year, we've earned in interest.
To find the **total value** after the first year, we **add** this interest to our **initial investment**:
STEP 6
For the second year, our **new starting amount** is , which includes the interest from the first year.
This is the beauty of **compound interest**!
STEP 7
We **calculate** the interest earned in the second year by **multiplying** this **new starting amount** by the same **interest rate** of :
STEP 8
Finally, we **add** this interest to our **starting amount** for the second year to find the **final value** after two years:
STEP 9
After 2 years, the investment will be worth .
Was this helpful?
