Lisa deposits $10,000 into an account that pays simple interest at a rate of 6% per year Scott deposits $10,000 into an account that also pays 6% interest per year but it is compounded annually find the interest Lisa and Scott earned during each of the first three years then decide who earns more interest for each year assume there are no withdrawals and no additional deposits
To calculate the simple interest earned by Lisa each year, we use the formula: Interest = Principal * Rate * Time.
For the first year:
Interest_Lisa_Year1 = $10,000 * 6% * 1 = $600.
For the second year:
Interest_Lisa_Year2 = $10,000 * 6% * 1 = $600.
For the third year:
Interest_Lisa_Year3 = $10,000 * 6% * 1 = $600.
Therefore, Lisa earns $600 in interest for each of the first three years.
To calculate the compound interest earned by Scott each year, we use the formula: Compound Interest = Principal * (1 + Rate)^Time - Principal.
For the first year:
Compound_Interest_Scott_Year1 = $10,000 * (1 + 6%)^1 - $10,000 = $600.
For the second year:
Compound_Interest_Scott_Year2 = $10,000 * (1 + 6%)^2 - $10,000 = $636.
For the third year:
Compound_Interest_Scott_Year3 = $10,000 * (1 + 6%)^3 - $10,000 = $676.16.
Therefore, Scott earns $600, $636, and $676.16 in compound interest for the first, second, and third years, respectively.
Comparing the interest earned by Lisa and Scott each year:
Year 1: Lisa earns $600 in simple interest, while Scott earns $600 in compound interest. They both earn the same amount.
Year 2: Lisa earns $600 in simple interest, while Scott earns $636 in compound interest. Scott earns more interest.
Year 3: Lisa earns $600 in simple interest, while Scott earns $676.16 in compound interest. Scott earns more interest.
In conclusion, Scott earns more interest than Lisa for the second and third year when considering compound interest. For the first year, they both earn the same amount of interest.
To calculate the interest earned by Lisa and Scott, we can use the simple interest formula for Lisa and the compound interest formula for Scott.
1. Year 1:
For Lisa:
The interest earned by Lisa in the first year can be calculated using the formula: Interest = Principal * Rate * Time
Interest = $10,000 * 0.06 * 1 = $600
For Scott:
To calculate the interest earned by Scott in the first year, we use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
Interest = A - P
Interest = $10,000 * (1 + 0.06/1)^(1*1) - $10,000
Interest ≈ $10,610 - $10,000 ≈ $610
In the first year, Scott earns more interest than Lisa.
2. Year 2:
For Lisa:
Since Lisa's account pays simple interest, the amount earned each year will remain the same.
Interest = $600
For Scott:
To calculate the interest earned by Scott in the second year, we use the compound interest formula again:
Interest = A - P
Interest = $10,610 * (1 + 0.06/1)^(1*2) - $10,000
Interest ≈ $11,275.16 - $10,000 ≈ $1,275.16
In the second year, Scott earns more interest than Lisa.
3. Year 3:
For Lisa:
Again, Lisa's account pays simple interest, so the amount earned each year remains the same.
Interest = $600
For Scott:
To calculate the interest earned by Scott in the third year:
Interest = A - P
Interest = $11,275.16 * (1 + 0.06/1)^(1*3) - $10,000
Interest ≈ $11,965.62 - $10,000 ≈ $1,965.62
In the third year, Scott earns more interest than Lisa.
Summary:
- Lisa earns $600 in interest each year.
- Scott earns $610, $1,275.16, and $1,965.62 in interest respectively in the first, second, and third year.
Based on the calculations, Scott earns more interest than Lisa each year.