d$)$ Isabella is struggling to pay her monthly debts. She approached her bank

recently and they recommended that she takes out a revolving credit loan of

$$45,000$ to consolidate all of her debts. The terms and conditions of this loan

states that the loan must be paid back monthly over $5$ years at a nominal rate of

$6\mathrm{.}5\%$ per year, compounded monthly. Determine:

The principal contained in the $25$ th payment.

The balance outstanding after the $50$ th payment.

The final payment $($with the adjustment$).$

e$)$ An amount of $5,000$ is invested at a fixed rate of $8$ per cent per annum. What

amount will be the value of the investment in $5$ years $\text{'}$ time, if the interest is

compounded:

i$)$ annually?

ii$)$ every $6$ months?