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anonymous

  • one year ago

The formula to find the amount in an account, A, that has an interest rate, r, that compounds n times per year and has a starting balance of P after t years is . If the interest is compounded yearly, then n = 1 and the interest rate, r, represents the annual interest. When the interest is compounded monthly, then n = 12 but r is still the annual interest. a. If you were given the equation , how often is the interest compounded?

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  1. kropot72
    • one year ago
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    \[\large A=P(1+\frac{r}{n})^{nt}\] where r is expressed as a decimal.

  2. kropot72
    • one year ago
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    a) The question states that the interest rate compounds n times per year.

  3. kropot72
    • one year ago
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    @Kaelyn78 Are you there?

  4. anonymous
    • one year ago
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    here

  5. anonymous
    • one year ago
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    thank you

  6. kropot72
    • one year ago
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    You're welcome :)

  7. anonymous
    • one year ago
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    b. If you were given the equation , what would the annual interest rate be?

  8. anonymous
    • one year ago
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    @kropot72

  9. kropot72
    • one year ago
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    As the question states "the interest rate, r, represents the annual interest".

  10. anonymous
    • one year ago
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    I don't get it

  11. kropot72
    • one year ago
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    "If you were given the equation , what would the annual interest rate be?" The annual interest rate is r in the equation that I posted. r must be expressed as a decimal. If the annual interest rate was 6%, r would be expressed as 0.06.

  12. kropot72
    • one year ago
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    @Kaelyn78 Is it any clearer now?

  13. anonymous
    • one year ago
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    yes that makes more sense

  14. anonymous
    • one year ago
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    c. What would need to change about the equation in part b for it to represent an account that is compounded monthly?

  15. kropot72
    • one year ago
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    If an account is compounded monthly, that means it compounds 12 times per year. Which variable in the equation represents the number of times in a year that the account compounds?

  16. kropot72
    • one year ago
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    The answer is in the question.

  17. anonymous
    • one year ago
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    you need to change r?

  18. kropot72
    • one year ago
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    Not really. The variables are A, r, n, P and t. Which one does the question use for "times per year"?

  19. kropot72
    • one year ago
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    The question states "When the interest is compounded monthly, then n = 12 but r is still the annual interest."

  20. anonymous
    • one year ago
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    so you need to change n?

  21. kropot72
    • one year ago
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    Therefore you would replace n by 12 in the equation to represent an account that is compounded monthly.

  22. kropot72
    • one year ago
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    Giving: \[\large A=P(1+\frac{r}{12})^{12t}\]

  23. anonymous
    • one year ago
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    that makes sense

  24. anonymous
    • one year ago
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    d. Use the properties of exponents to rewrite the equation given in part b so that it represents an account that is compounded monthly.

  25. kropot72
    • one year ago
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    The required equation was posted above.

  26. anonymous
    • one year ago
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    thank you

  27. anonymous
    • one year ago
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    e. What would be the approximate monthly interest rate that is equivalent to the annual interest rate represented in the equation given in part b?

  28. kropot72
    • one year ago
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    The approximate monthly interest rate that is equivalent to the annual interest rate represented in the equation given in part b is r/12.

  29. anonymous
    • one year ago
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    thank you for all your help

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