Question
Compare simple interest at 7.5% and compound interest at 7.0% when $4,300 is invested for 2 years
to determine which interest earning type will result in a higher balance. Find this balance
to determine which interest earning type will result in a higher balance. Find this balance
Answers
GPT 3.5
To compare the simple interest and compound interest, we need to calculate the balances for both scenarios.
For simple interest, the formula is:
Simple Interest = P * r * t
Where:
P = Principal amount (initial investment) = $4,300
r = Interest rate = 7.5% = 0.075
t = Time in years = 2
Simple Interest = $4,300 * 0.075 * 2 = $645
The balance with simple interest after 2 years will be the principal plus the simple interest:
Balance with Simple Interest = $4,300 + $645 = $4,945
For compound interest, the formula is:
Compound Interest = P * (1 + r/n)^(n * t) - P
Where:
P = Principal amount (initial investment) = $4,300
r = Interest rate = 7.0% = 0.07
n = Number of times interest is compounded per year (assuming annually) = 1 (since it is compounded once a year)
t = Time in years = 2
Compound Interest = $4,300 * (1 + 0.07/1)^(1 * 2) - $4,300
Using a calculator, the compound interest is approximately $645.71.
The balance with compound interest after 2 years will be the principal plus the compound interest:
Balance with Compound Interest = $4,300 + $645.71 = $4,945.71
Therefore, the balance with compound interest at 7.0% after 2 years will be slightly higher than the balance with simple interest at 7.5%. The balance will be $4,945.71.
For simple interest, the formula is:
Simple Interest = P * r * t
Where:
P = Principal amount (initial investment) = $4,300
r = Interest rate = 7.5% = 0.075
t = Time in years = 2
Simple Interest = $4,300 * 0.075 * 2 = $645
The balance with simple interest after 2 years will be the principal plus the simple interest:
Balance with Simple Interest = $4,300 + $645 = $4,945
For compound interest, the formula is:
Compound Interest = P * (1 + r/n)^(n * t) - P
Where:
P = Principal amount (initial investment) = $4,300
r = Interest rate = 7.0% = 0.07
n = Number of times interest is compounded per year (assuming annually) = 1 (since it is compounded once a year)
t = Time in years = 2
Compound Interest = $4,300 * (1 + 0.07/1)^(1 * 2) - $4,300
Using a calculator, the compound interest is approximately $645.71.
The balance with compound interest after 2 years will be the principal plus the compound interest:
Balance with Compound Interest = $4,300 + $645.71 = $4,945.71
Therefore, the balance with compound interest at 7.0% after 2 years will be slightly higher than the balance with simple interest at 7.5%. The balance will be $4,945.71.