Sally Jones invests $$800$ at $5\%$ compounded annually.

a$.$ Use the rule of $72$ to estimate how many years it will take her

investment to double in value. $(1$ mark$)$

b$.$ Use the compound interest formula to determine the actual value of

$$800$ at $5\%$ compounded annually for the number of years you

determined in part a$.(2$ marks$)$

c$.$ Calculate the difference between the actual value of the investment

and the doubled value found using the rule of $72.(1$ mark$)$