anonymous
  • anonymous
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?
Mathematics
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chestercat
  • chestercat
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kropot72
  • kropot72
\[\large A=P(1+\frac{r}{n})^{nt}\] where r is expressed as a decimal.
kropot72
  • kropot72
a) The question states that the interest rate compounds n times per year.
kropot72
  • kropot72
@Kaelyn78 Are you there?

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anonymous
  • anonymous
here
anonymous
  • anonymous
thank you
kropot72
  • kropot72
You're welcome :)
anonymous
  • anonymous
b. If you were given the equation , what would the annual interest rate be?
anonymous
  • anonymous
@kropot72
kropot72
  • kropot72
As the question states "the interest rate, r, represents the annual interest".
anonymous
  • anonymous
I don't get it
kropot72
  • kropot72
"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.
kropot72
  • kropot72
@Kaelyn78 Is it any clearer now?
anonymous
  • anonymous
yes that makes more sense
anonymous
  • anonymous
c. What would need to change about the equation in part b for it to represent an account that is compounded monthly?
kropot72
  • kropot72
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?
kropot72
  • kropot72
The answer is in the question.
anonymous
  • anonymous
you need to change r?
kropot72
  • kropot72
Not really. The variables are A, r, n, P and t. Which one does the question use for "times per year"?
kropot72
  • kropot72
The question states "When the interest is compounded monthly, then n = 12 but r is still the annual interest."
anonymous
  • anonymous
so you need to change n?
kropot72
  • kropot72
Therefore you would replace n by 12 in the equation to represent an account that is compounded monthly.
kropot72
  • kropot72
Giving: \[\large A=P(1+\frac{r}{12})^{12t}\]
anonymous
  • anonymous
that makes sense
anonymous
  • anonymous
d. Use the properties of exponents to rewrite the equation given in part b so that it represents an account that is compounded monthly.
kropot72
  • kropot72
The required equation was posted above.
anonymous
  • anonymous
thank you
anonymous
  • anonymous
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?
kropot72
  • kropot72
The approximate monthly interest rate that is equivalent to the annual interest rate represented in the equation given in part b is r/12.
anonymous
  • anonymous
thank you for all your help

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