We know that the Compound Interest Formula is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where A is the amount,
P is the Principal,
r is the interest rate in decimal
n is the number of times interest is compounded per year
t is the number of years.
In our case we will have to find the Amount, A in one year when the principal, P is compounded quarterly at a rate of 6% and compare it with the amount when the same principal is compounded monthly at a rate of 1.25% monthly and see if they are equal or not and explain the possible reason.
Let us begin:
Case 1
6% Quarterly
[tex]A=P(1+\frac{0.006}{4})^{4\times 1}=P(1+0.0015)^4\approx1.006P[/tex]
Case 2
1.25% Monthly
[tex]A=P(1+\frac{0.0125}{12})^{12\times 1}=P(1+0.00104167)^{12}\approx1.0126P[/tex]
As we can clearly see the first case gives us 1.006P and the second case gives us 1.0126P.
Therefore, Naomi is incorrect in her reasoning. This can be seen from the fact that the [tex]\frac{r}{n}[/tex] and the [tex]n\times t[/tex] are coming out to be different for both the cases and thus effecting the overall results.
