Between simple interest at 9.2% and compound interest at 7.8% with interest being compounded semiannually, determine which interest earning type will result in a higher balance when $10,000 is invested for 15 years. Find the difference in interest earnings between the two interest earning types.
A: Compound interest at 7.8% is the better interest earning type. The difference in interest earnings is $9,811.31.
B: Simple interest at 9.2% is the better interest earning type. The difference in interest earnings is $14,743.45.
C: Compound interest at 7.8% with interest being compounded semiannually is the better interest earning type. The difference in interest earnings is $7,711.31.
D: Compound interest at 7.8% with interest being compounded semiannually is the better interest earning type. The difference in interest earnings is $7,051.86.
To determine which interest earning type will result in a higher balance, we need to calculate the final balance for each option.
For simple interest at 9.2%:
Simple Interest = Principal * Rate * Time
= $10,000 * 0.092 * 15
= $13,800
For compound interest at 7.8% with interest being compounded semiannually:
Compound Interest = Principal * (1 + Rate/2)^(2*Time)
= $10,000 * (1 + 0.078/2)^(2*15)
= $17,511.31
The difference in interest earnings between the two options would be:
$17,511.31 - $13,800 = $3,711.31
Therefore, option C: Compound interest at 7.8% with interest being compounded semiannually is the better interest earning type. The difference in interest earnings is $3,711.31.