Emma plans to loan $$1,000$ to her friend, who will pay a simple interest rate of $5\mathrm{.}8\%$ every year for the loan. If no payments are made and no further borrowing occurs between them for $13$ years, then how much money will Emma$$s friend owe her?

$$1,061\mathrm{.}36$

$$1,754\mathrm{.}00$

$$2,081\mathrm{.}20$

$$158\mathrm{.}00$

Now, assume that Emma$$s friend volunteers to pay compound interest instead of simple interest for her loan. If interest is accrued at $5\mathrm{.}8\%$ compounded annually, all other things being equal, how much money will Emma$$s friend owe her in $13$ years?

$$2,081\mathrm{.}20$

$$1,058\mathrm{.}00$

$$120\mathrm{.}71$

$$1,754\mathrm{.}00$

Emma has another investment option in the market that pays $5\mathrm{.}8\%$ nominal interest, but it$$s compounded quarterly. Keeping everything else constant, how much money will Emma have in $13$ years if she invests $$1,000$ in this fund?

$$158\mathrm{.}00$

$$129\mathrm{.}72$

$$2,114\mathrm{.}01$

$$1,059\mathrm{.}27$