Respuesta :
Mr Guny deposits $45,900 in a savings account
Principal, P = $45,900
Annual rate, R = 1.5%
Time, t = 1 year since it is componded quarterly,
Interest rate, r will be
[tex]\begin{gathered} r=\frac{R}{100} \\ \text{Where R}=1.5\text{\%} \\ r=\frac{1.5}{100}=0.015 \\ r=0.015 \end{gathered}[/tex]a) To find the first quarter's interest,
[tex]\begin{gathered} I=P(\frac{r}{n}) \\ \text{Where P}=\text{\$45,900} \\ r=0.015\text{ and } \\ n=4 \end{gathered}[/tex]Substitute the values into the above expression
[tex]\begin{gathered} I=45900\times\frac{0.015}{4}=\frac{45900\times3}{800}=172.125 \\ I=\text{\$172.125} \end{gathered}[/tex]Hence, the first quarter's interest is $172.125
b) The first quarter's balance, A, will be
[tex]\begin{gathered} A=P+I \\ \text{Where } \\ P=\text{\$45900} \\ I=\text{\$172.125} \end{gathered}[/tex]Substitute the values into the formula above
[tex]\begin{gathered} A=P+I \\ A=45900+172.125=46072.125 \\ A=\text{\$}46072.125 \end{gathered}[/tex]Hence, the first quarter's balance is $46,072.125
