Question

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. Please help me!! It’s due today!! I’ll make you brainliest.

Answer 1

Answer:Yes, Naomi is incorrect.

Explanation: For explain this we can consider an example - Let us suppose Naomi deposited 100 rupees in her saving account at the rate 6% for 1 year .

Now, if the interest is quarterly then according to the formula

compound interest =$P(1+\frac{r/4}{100} )^{4n}$ -P where r is the rate annually and n is the number of years.

so CI=$100(1+\frac{6}{100})^4$ -100 ( here the rate is already given in quarterly)

CI= $100(1.06)^4$-100= 1.26247696-100=26.247696 rupees=26(approx)

Now, if the compound interest is 1.25 per month then again from the formula-

CI=$P(1+\frac{r/12}{100})^{12n}$-P

CI= $100(1+\frac{1.25}{100})^{12}$-100= 100(1.16075452)-100=16.075452=16(approx)