You deposit $500 in an account that earns 4% simple annual interest. The interest earned each year is added to the principal to create a new principal. Find the total amount in your account after each year for 3 years.
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1 520
2 540.80
3 562.43
To find the total amount in your account after each year for 3 years, you need to calculate the interest earned each year and add it to the principal.
First, let's calculate the interest earned each year. The formula for calculating simple interest is:
Interest = Principal × Rate × Time
In this case, the principal is $500, the rate is 4%, and the time is 1 year. Substituting these values into the formula:
Interest = $500 × 0.04 × 1 = $20
So, you earn $20 in interest in the first year.
To find the total amount in your account after the first year, you need to add the interest earned to the principal:
Total amount after year 1 = Principal + Interest = $500 + $20 = $520
Now, for the second year, you will use the new principal of $520 to calculate the interest earned:
Interest = $520 × 0.04 × 1 = $20.80
So, you earn $20.80 in interest in the second year.
To find the total amount in your account after the second year, you need to add the interest earned to the principal:
Total amount after year 2 = Principal + Interest = $520 + $20.80 = $540.80
Finally, for the third year, you will use the new principal of $540.80 to calculate the interest earned:
Interest = $540.80 × 0.04 × 1 = $21.63 (rounded to two decimal places)
So, you earn $21.63 in interest in the third year.
To find the total amount in your account after the third year, you need to add the interest earned to the principal:
Total amount after year 3 = Principal + Interest = $540.80 + $21.63 = $562.43 (rounded to two decimal places)
Therefore, the total amount in your account after each year for 3 years would be as follows:
- After the first year: $520
- After the second year: $540.80
- After the third year: $562.43
500 * 1.04^3
This is just compound interest