Problem:
Mrs. Johns has a 5-year-old son, Mike. He has been watching too much MTV, and refuses to listen to her unless she promises him a flashy Ferrari for a high school graduation gift. Luckily, she has some extra cash from her tax return refund she is willing to invest for Mike.
1. If her spoiled son is expected to graduate from high school in 12 years, how much would Mrs. Johns have to deposit right now without any further payments to accumulate $40,000 by the time Mike graduates? Assume her bank offers 6% interest compounded annually.
2. If another bank offered her a simple interest rate of 8%, should Mrs. Johns accept this offer over her current bank?
3. What rate, in simple interest terms, would the second bank need to offer to Mrs. Johns to entice her to switch banks?
4. Assuming Mike graduates in 18 years, how much she needs to deposit today to have $40,000 assuming she earns 4% compounded monthly and that she deposits $25 monthly, as well. Assume she begins saving when he is born.
Show all work and explain in detail.