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.(1 point)
The difference in interest earnings is $
.
The simple interest earned can be calculated using the formula:
Simple Interest = Principal * Interest Rate * Time
Simple Interest = $25,000 * 0.10 * 25 = $62,500
For compound interest, the formula is:
Compound Interest = P(1 + r/n)^(nt) - P
Where P is the principal ($25,000), r is the interest rate (0.07), n is the number of times interest is compounded per year (1 in this case), and t is the number of years (25).
Compound Interest = $25,000(1 + 0.07/1)^(1*25) - $25,000
Compound interest = $25,000 * (1.07)^(25) - $25,000
Using a calculator, the compound interest is approximately $164,494.07
Difference in interest earnings = Compound Interest - Simple Interest
Difference in interest earnings = $164,494.07 - $62,500
Difference in interest earnings = $101,994.07
Therefore, the difference in interest earnings between a 10% simple interest rate and a 7% compound interest rate over 25 years is approximately $101,994.07.