Compare simple interest at 3% and compound interest at 2% with interest being compounded monthly when $750 is invested for 1 year to determine which interest earning type offers more financial gains.
a. There is not enough information to determine which interest earning type offers more financial gains.
b. Compound interest at 2% offers more financial gains.
c. Simple interest at 3% offers more financial gains.
d. Both simple interest at 3% and compound interest at 2% with interest being compounded monthly offer the same amount of financial gain after 1 year of investment.
To compare the financial gains from simple interest at 3% and compound interest at 2% with interest being compounded monthly, we need to calculate the amount earned in each case.
For simple interest at 3%, the formula for calculating the interest is:
Interest = Principal * Rate * Time
In this case, the principal is $750, the rate is 3%, and the time is 1 year. Plugging these values into the formula, we get:
Interest = $750 * 0.03 * 1 = $22.50
So, with simple interest at 3%, the investor would earn $22.50 in 1 year.
For compound interest at 2% with interest being compounded monthly, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Amount after time t
P = Principal
r = Annual interest rate
n = Number of times interest is compounded per year
t = Time in years
In this case, the principal is $750, the rate is 2%, the interest is compounded monthly (n = 12), and the time is 1 year. Plugging these values into the formula, we get:
A = $750(1 + 0.02/12)^(12*1) ≈ $762.30
So, with compound interest at 2% compounded monthly, the investor would earn approximately $762.30 in 1 year.
Comparing the two amounts earned, we can see that compound interest at 2% offers more financial gains ($762.30) compared to simple interest at 3% ($22.50). Therefore, the correct answer is b. Compound interest at 2% offers more financial gains.