Final answer:
Jenny will earn $50.39 more in interest by investing $500 at a 4.25% rate compounded annually for 10 years, compared to earning interest through a simple interest calculation.
Step-by-step explanation:
To calculate how much more interest Jenny will earn by investing $500 at a 4.25% compounded annually rate for 10 years compared to simple interest, we need to use the formulas for both compounding and simple interest.
For compound interest, the formula is A = P(1 + r/n)^(nt), where:
- P is the principal amount ($500)
- r is the annual interest rate (4.25%, or 0.0425)
- n is the number of times interest is compounded per year (1, since it's compounded annually)
- t is the number of years (10)
So, for compound interest, we calculate:
500(1 + 0.0425/1)^(1*10) = 500(1.0425)^10 = $762.89 approximately.
For simple interest, the formula is A = P(1 + rt), where:
- r again is the annual interest rate (0.0425)
- t is the time in years (10)
Therefore, for simple interest, we calculate:
500(1 + 0.0425*10) = 500(1 + 0.425) = $712.50 approximately.
The difference in interest earned through compound interest versus simple interest is thus $762.89 - $712.50 = $50.39 more with compound interest.