You are hoping to buy a house in the future and recently received an inheritance of $$$$18,000.$ You intend to use your inheritance as a down payment on your house.

a$.$If you put your inheritance in an account that earns $8$ percent interest compounded$$ annually, how many years will it be before your inheritance grows to $$$$30,000?$

b$.$If you let your money grow for $9\mathrm{.}75$ years at $8$ percent$,$ how much will you$$ have?

c$.$How long will it take your money to grow to $$$$30,000$ if you move it into an account that pays $5$ percent compounded$$ annually? How long will it take your money to grow to $$$$30,000$ if you move it into an account that pays $13$ percent$?$

d$.$What does all this tell you about the relationship among interest$$ rates, time, and future$$ sums?