Jessica deposits $50,000 into an account that pays 4% interest per year compounded annually Tom deposits $50,000 into an account that also pays 4% per year but it is simple interest find the interest Jessica and Tom earn 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 interest earned by Jessica each year, we can use the formula for compound interest:
Compound interest = Principal * (1 + interest rate)^time - Principal
For the first year:
Principal = $50,000
Interest rate = 4% = 0.04
Time = 1 year
Compound interest = $50,000 * (1 + 0.04)^1 - $50,000
Compound interest = $50,000 * (1.04) - $50,000
Compound interest = $52,000 - $50,000
Compound interest = $2,000
For the second year:
Principal = $50,000
Interest rate = 4% = 0.04
Time = 2 years
Compound interest = $50,000 * (1 + 0.04)^2 - $50,000
Compound interest = $50,000 * (1.04)^2 - $50,000
Compound interest = $50,000 * (1.0816) - $50,000
Compound interest = $54,080 - $50,000
Compound interest = $4,080
For the third year:
Principal = $50,000
Interest rate = 4% = 0.04
Time = 3 years
Compound interest = $50,000 * (1 + 0.04)^3 - $50,000
Compound interest = $50,000 * (1.04)^3 - $50,000
Compound interest = $50,000 * (1.1259) - $50,000
Compound interest = $56,295 - $50,000
Compound interest = $6,295
Now let's calculate the interest earned by Tom each year using the formula for simple interest:
Simple interest = Principal * interest rate * time
For the first year:
Principal = $50,000
Interest rate = 4% = 0.04
Time = 1 year
Simple interest = $50,000 * 0.04 * 1
Simple interest = $2,000
For the second year:
Principal = $50,000
Interest rate = 4% = 0.04
Time = 2 years
Simple interest = $50,000 * 0.04 * 2
Simple interest = $4,000
For the third year:
Principal = $50,000
Interest rate = 4% = 0.04
Time = 3 years
Simple interest = $50,000 * 0.04 * 3
Simple interest = $6,000
Comparing the interest earned by Jessica and Tom each year:
Year 1: Jessica earns $2,000 in compound interest, while Tom earns $2,000 in simple interest.
Jessica earns the same interest as Tom.
Year 2: Jessica earns $4,080 in compound interest, while Tom earns $4,000 in simple interest.
Jessica earns more interest than Tom.
Year 3: Jessica earns $6,295 in compound interest, while Tom earns $6,000 in simple interest.
Jessica earns more interest than Tom.
In summary, Jessica earns more interest during the second and third years, while they earn the same interest during the first year.
To determine the interest earned by Jessica and Tom, we can use the formulas for compound interest and simple interest.
First, let's calculate the interest earned by Jessica for the first three years using compound interest:
Year 1:
Interest = Principal x Rate
Interest = $50,000 x 0.04
Interest = $2,000
Year 2:
New principal = Principal + Interest
New principal = $50,000 + $2,000
Interest = New principal x Rate
Interest = $52,000 x 0.04
Interest = $2,080
Year 3:
New principal = Principal + Year 2 Interest
New principal = $50,000 + $2,000 + $2,080
Interest = New principal x Rate
Interest = $54,080 x 0.04
Interest = $2,163.20
Now, let's calculate the interest earned by Tom for the first three years using simple interest:
Year 1:
Interest = Principal x Rate
Interest = $50,000 x 0.04
Interest = $2,000
Year 2:
Interest = Principal x Rate
Interest = $50,000 x 0.04
Interest = $2,000
Year 3:
Interest = Principal x Rate
Interest = $50,000 x 0.04
Interest = $2,000
Now, let's compare the interest earned by Jessica and Tom for each year:
Year 1: Jessica earns $2,000 in interest, Tom earns $2,000 in interest.
Year 2: Jessica earns $2,080 in interest, Tom earns $2,000 in interest.
Year 3: Jessica earns $2,163.20 in interest, Tom earns $2,000 in interest.
From the calculations, we can see that Jessica earns more interest than Tom for the first three years.