## 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?

1. kropot72

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

2. kropot72

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

3. kropot72

@Kaelyn78 Are you there?

4. anonymous

here

5. anonymous

thank you

6. kropot72

You're welcome :)

7. anonymous

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

8. anonymous

@kropot72

9. kropot72

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

10. anonymous

I don't get it

11. 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.

12. kropot72

@Kaelyn78 Is it any clearer now?

13. anonymous

yes that makes more sense

14. anonymous

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

15. 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?

16. kropot72

The answer is in the question.

17. anonymous

you need to change r?

18. kropot72

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

19. kropot72

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

20. anonymous

so you need to change n?

21. kropot72

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

22. kropot72

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

23. anonymous

that makes sense

24. 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.

25. kropot72

The required equation was posted above.

26. anonymous

thank you

27. 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?

28. 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.

29. anonymous

thank you for all your help