Serenity wants to invest $25,000 of her savings for her retirement fund. Determine the difference in interest earnings between a 10% simple interest rate and a 7% compound interest rate with interest being compounded annually if Serenity invests her money for 25 years. Round the answer to two decimal places as needed.
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The formula for calculating simple interest is I = P * r * t, where I is the interest, P is the principal (initial investment), r is the interest rate, and t is the time in years.
For the 10% simple interest rate, the interest earned after 25 years would be I = 25000 * 0.1 * 25 = $62500.
To calculate compound interest, we use the formula A = P * (1 + r/n)^(n*t), where A is the amount accumulated after time t, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.
For the 7% compound interest rate compounded annually, the interest earned after 25 years would be A = 25000 * (1 + 0.07/1)^(1*25) = $100370.67.
The difference in interest earnings is $100370.67 - $62500 = $37870.67.
Therefore, the difference in interest earnings between a 10% simple interest rate and a 7% compound interest rate after 25 years is $37,870.67. Answer: \boxed{37870.67}.