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 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.