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?

Question

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?

kropot72 · Answer

$$\large A=P(1+\frac{r}{n})^{nt}$$
where r is expressed as a decimal.

kropot72 · Answer

a) The question states that the interest rate compounds n times per year.

kropot72 · Answer

@Kaelyn78 Are you there?

anonymous · Answer

here

anonymous · Answer

thank you

kropot72 · Answer

You're welcome :)

anonymous · Answer

b.	If you were given the equation , what would the annual interest rate be?

anonymous · Answer

@kropot72

kropot72 · Answer

As the question states "the interest rate, r, represents the annual interest".

anonymous · Answer

I don't get it

kropot72 · Answer

"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 · Answer

@Kaelyn78 Is it any clearer now?

anonymous · Answer

yes that makes more sense

anonymous · Answer

c.	What would need to change about the equation in part b for it to represent an account that is compounded monthly?

kropot72 · Answer

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 · Answer

The answer is in the question.

anonymous · Answer

you need to change r?

kropot72 · Answer

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

kropot72 · Answer

The question states "When the interest is compounded monthly, then n = 12 but r is still the annual interest."

anonymous · Answer

so you need to change n?

kropot72 · Answer

Therefore you would replace n by 12 in the equation to represent an account that is compounded monthly.

kropot72 · Answer

Giving:
$$\large A=P(1+\frac{r}{12})^{12t}$$

anonymous · Answer

that makes sense

anonymous · Answer

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 · Answer

The required equation was posted above.

anonymous · Answer

thank you

anonymous · Answer

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 · Answer

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 · Answer

thank you for all your help