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

Answer 1

Answer: No, She is not correct.

Step-by-step explanation:

Let P is the principle amount of the money.

Then, the compound interest amount after 1 year with the compound quarterly rate of 6% is,

$A = P( 1+6/100)^4$ ( By the formula, $A = P( 1+\frac{r/n}{100})^{nt}$)

⇒ $A = 1.26247696 P$

And, the compound interest amount after 1 year with the compound monthly rate of 1.25% is,

$A = P( 1+1.25/100)^{12}$

$A = 1.16075451772 P$

Therefore, By both interests rate we are getting different amounts.

Thus, there is a mistake in her calculation.