$1.$ Rather than invest in the savings account or mutual fund, your sister gave you a third alternative: the opportunity to invest in her new business. If you loan her $$12,000$ today, she will pay you $$1,400$ at the end of each of the next $10$ years $($total payments $=$ $$14,000).$ What is the value of her investment to you today assuming you want to earn at least $8\%$ compounded annually you could earn by investing in the fixed income investment fund?

$2.$ You want to help your sister out and are willing to invest in her business, but you also realize it is more risky than a high grade diversified fixed income investment fund and you want to earn a premium for taking on risk. You believe your return from here should be $10\%,$ which is a $2\%$ risk premium above the expected you expect to earn in the diversified fixed income mutual fund. What is the minimum annual amount you should agree to$?$