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

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

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