Naomi deposited money into a savings account that is compounded quarterly at an interest rate of 6%. she thinks this quarterly rate is the same as a monthly interest rate of 1.25%. is naomi right? if so, explain why and show how you got your answer. is naomi incorrect? if so, explain the mistake in her reasoning, give the correct monthly interest rate, and show how you got your answer. it’s due today

Given that Naomi deposited some money into a savings account that is compounded quarterly at an interest rate of 6%.

Now we have to identify if the compounded quarterly interest rate is same as monthly interest rate or not.

We know that future value of compound interest formula is given by:

Where P= initial deposit

r = yearly rate of interest = 6%= 0.06

n = number of compounding per year

For quarterly n=4 because there are 4 quarters in 1 year.

For monthly n=12 because there are 12 months in 1 year.

t= number of years.

We know that there are 4 months in 1 quarter so to convert quarterly rate into monthly rate, we need to divide quarterly rate by 4 so we get

monthly rate = 6%/4= 1.25 %

while the given interest rate is 1.5% which is different than obtained value 1.25%

Hence Naomi is thinking WRONG that  this quarterly rate is the same as a monthly interest rate of 1.25%.

Correct monthly interest rate will be 1.5% as shown above.