Sarah's Lashes Business is currently valued at $$100,000.$ Sarah feels the value of her business will increase at a rate of $10\%$ per year, compounded semiannually for the next $5$ years. One of her competitors Pink Lashes offered her $$110,000$ for the business. If she sells, Sarah plans to invest the money for $6\%$ compounded quarterly. What do you think Sarah should do$?$ Explain in details, in$-$terms of future value of business, or if she took the money would she potentially earn the same amount on $5$ years or more.