Problem $5\mathrm{.}1$: Assume your Grandfather just sold his old $1957$ Chevy for $$50,000.$ He has decided to gift you the proceeds and you are then going to invest all this money. Consider the value for each of the below scenarios.

a$.$ Calculate the amount of money that will accumulate if you leave the money in a bond fund for $5,10,$ and $20$ years and the fund pays an annual compound interest of $5\%.$

b$.$ Now suppose you decide to get more aggressive with your money and invest the $$50,000$ into a stock fund that pays $8\%$ annual compound interest. Or a high growth stock fund that pays $10\%$ annual compound interest. Calculate the value for each of these scenarios if you invest for the same $5,10$ and $20$ years.

c$.$ What conclusions can you draw about the relationship among interest rates, time, and future sums from the calculations you just did?