At a nominal interest rate of $i^{(2)}$ convertible semi$-$annually, an investment of $1000$ immediately

and $1500$ at the end of the first year will accumulate to $2600$ at the end of the second year.

Under the same interest rate, what is the present value of $1000$ paid at the end of the fifth

year? $($Hint: one needs to evaluate $(1+\frac{i^{(2)}}{2}{)}^2$ as a whole.$)$

At a nominal interest rate of $i^{(2)}$ convertible semi$-$annually, an investment of $1000$ immediately

and $1500$ at the end of the first year will accumulate to $2600$ at the end of the second year.

Under the same interest rate, what is the present value of $1000$ paid at the end of the fifth

year? $($Hint: one needs to evaluate $(1+\frac{i^{(2)}}{2}{)}^2$ as a whole.$)$