If we use m compounded per year Bt will be to:
[tex]\begin{gathered} B_t=B_0(1+\frac{r}{m})^{mt} \\ I_t=B_t-B_0 \end{gathered}[/tex]Where:
B0 = deposits = $45900
r = compound yearly interest rate = 1.5% = 0.015
t = years
m = 4
The first quarter's interest
We have following:
[tex]\begin{gathered} B_t=45900\cdot(1+\frac{0.015}{4})^{4\cdot\frac{3}{12}} \\ B_t=45900\cdot(1+\frac{0.015}{4})^1 \\ B_t=46072.13 \end{gathered}[/tex]Then:
[tex]I_{1th\text{ quarter}}=46072.125-45900=172.13[/tex]Answer: The interest in first quarter is $172.13
The first quarter's balance
The balance is Bt, therefore:
Answer: The balance after first quarter is $46,072.13
