An investor with an initial endowment of $$16,000$ is confronted with the following productivity curve:

$C_1=240(16,000-C_0{)}^{0\mathrm{.}5}$

where C$0$ denotes consumption at present, and C$1$ consumption in the future. Assume the interest rate $($for borrowing and lending$)$ is $20\%.$ The investor's utility function, from which it is possible to derive his indifference curves, is defined as:

$U(C_0,C_1)=C_0{C}_1$

How much does the investor borrow or lend in the capital market?

A$)$ The investor borrowed $$13,000$

B$)$ The investor lent $$13,000$

C$)$ The investor borrowed $$7,000$

D$)$ The investor lent $$7,000$