In order to calculate the amount of money, we can use the formula:
[tex]P=P_0(1+\frac{i}{n})^{nt}[/tex]Where P0 is the initial amount, P is the final amount after t years, i is the interest rate and n depends on the compound period.
i)
If the interest is compounded quarterly, we can use n = 4, so:
[tex]\begin{gathered} P=250000\cdot(1+\frac{0.065}{4})^{4\cdot\frac{64}{12}} \\ P=250000(1.01625)^{\frac{64}{3}} \\ P=352602.40 \end{gathered}[/tex]b)
If the interest is compounded monthly, we have n = 12, so:
[tex]\begin{gathered} P=250000(1+\frac{0.065}{12})^{12\cdot\frac{64}{12}} \\ P=250000\cdot(1.00541667)^{64} \\ P=353255.67 \end{gathered}[/tex]