Rosalee has recently received a bonus of $12,000$ from her employer. She

plans to use this amount as down payment for her first house.

a$.$ If she puts this money in an account earning $8$ percent interest rate compounded annu ally, how many years will it take for her investment to be worth E$18,000?$

b$.$ If she invests in an account with a $10$ percent annual return and lets it grow for $7$ years, how much will she receive at the end of her investment period?

c$.$ She wants her money to grow to $18,000,$ how long will it take if she invests it in an account paying $4$ percent compounded annually? How long will it take if she invests in an account paying $12$ percent?

d$.$ What inferences can you derive from your calculations in the above three questions regarding the relationship between interest rates, time, and future sums?