Question 1: Ali goes to the bank to take out a personal loan. The stated annual interest rate is 12%, but interest is compounded monthly and he will make monthly payments. The effective annual interest rate (EAR) of the loan is less than 12%. True or false? and why?
Question 2: Ali began setting aside $6,000 per year in a mutual fund at the age of 25. He has turned 34, and has just made a deposit. The mutual fund has returned 6.5% annually. How much does Rajit have in his account today?
Question 3: Sara has just turned 65 and she has deposited her annual payment of $20,000 into her retirement account. She made her first such saving deposit into this fund on her 35th birthday. Sara has also retired and wants to figure out how much money she has in her retirement account for her retired life. You are Sara's friend who knows finance. How much is Sara's savings worth today given that the fund has earned an annual return of 5.5%?
Question 4: Ali has estimated that he is going to need enough in his retirement fund to withdraw $75,000 per year beginning on his 66th birthday and for 19 additional years thereafter. How much will Ali need in his retirement account at age 65 if his fund is expected to earn an annual return of 9.5%?
Question 5: Hueling owns a rental property on Main street, but she is considering selling the property to another real estate investor. In preparation for negotiating a price, Hueling wants to know the value of the property. The Net Operating Income (NOI) is the cash flow from real estate and the Cap Rate is the rate, where NOI is rental revenue less all expenses except loan servicing. The property has an NOI of $12,000 per year. The local real estate market has a cap rate of 6%. What is a fair price for the property assuming that the building's life is 35 years?
Question 6: Sara is in the market for a new house, and she has found a house she likes that is selling for $250,000. The down payment on the house is 20% (the amount that the bank should require you to pay in cash) & Sara plans to finance the remainder with a fixed rate mortgage. The annual rate is 6% and the mortgage is for 15 years, though payments are monthly. What is the interest component of Sara's first monthly payment?
Question 7: Ali, who has just celebrated her 29th birthday, will retire on her 55th birthday, and she has just set up a retirement plan to pay her income starting on her retirement day, & to continue paying for 19 more years. Ali's goal is to receive $120,000 for each of these twenty years. In creating her retirement account,
Ali has committed to set aside equal payments at the end of each year, for the next 25 years starting on her 30th birthday. If the annual interest rate is 9%, how big should Ali's equal payments be?
Question 8: Sara bought a house 10 years ago for $200,000. Her down payment on the house was the minimum required 10% at that time she financed the remainder with a 15-year fixed rate mortgage. The annual interest rate was 10% and she was required to make monthly payments, and she has just made her 120th payment. A new bank has offered to refinance the remaining balance on Sara's loan and she will have to pay $1,900 per month for the next 5 years, but the total fees she will have to pay today to get the new loan is $1,000. Should she take the new offer? How much will she gain or lose in today's dollars if she does? Annual interest rates are still 10%.
Question 9: You are interested in a new Ford Taurus. After visiting your Ford dealer, doing your research on the best leases available, you have three options. (i) Purchase the car for cash and receive a $1,500 cash rebate from Dealer A. The price of the car is $15,000. (ii) Lease the car from Dealer B. Under this option, you pay the dealer $500 now and $200 a month for each of the next 36 months (the first $200 payment occurs 1 month from today). After 36 months you may buy the car for $8,000. (iii) Purchase the car from Dealer C who will lend you the entire purchase price of the car for a zero interest 36-month loan with monthly payments. The car price is $15,000. Suppose the market interest rate is 6%. What is the net cost today of the cheapest option?