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Jenny is saving for a vacation to the beach. How much more interest will she earn if she invests $500 at 4.25% compounded annually for 10 years compared to simple interest? Explain your calculations.

User Kgoutsos
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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.

User Josep Panadero
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