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:
[tex]A=P\left(1+\frac{r}{n}\right)^{\left(nt\right)}[/tex]
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 3 months in 1 quarter so to convert quarterly rate into monthly rate, we need to divide quarterly rate by 3 so we get
monthly rate = 6%/3= 2 %
while the given interest rate is 1.5% which is different than obtained value 2%
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 2% as shown above.
