FIN331Fall 2010 Extra CreditDr. Rhee1. PVIF(10%, 1)?a. 0.909b. 1c. 1.1d. 1.21e. 1.331Answer: a1/(1.1)= 0.9092. What is the relationship between FVIF(r%, N) and PVIF(r%, N)?a. PVIF is greater than FVIFb. FVIF is a sum of PVIF from n=1 to n=Nc. PVIF is an inverse of FVIF d. PVIF is used for an annuitye. FVIF*PVIF=2.0 Answer: cFVIFA(r%, n) = sum of FVIF from t=1 to t=n, PVIFA(r%, n) = sum of all PVIF from t=1 to t=n, PVIF and FVIF have an inverse relationship. PVIF*FVIF=1.03. You want to buy a $15,000 car. If you borrow money from the dealer, they are willing to give you a 1 year loan and you need to make a single payment one year from today at zero interest. If you borrow money from a bank for the same one year period and make a cash payment to the dealer right now (using the money you borrow from the bank), you can enjoy a $1,000 discount from a dealer. The bank interest rate is 12% and you need to make a single payment one year from today to pay off the debt. Which alternative do you like better. Basically, you need to borrow money, either from the dealer or from the bank. What is the difference between the future payments of these two choices?a. Loan from the dealer, more than $2,000b. Bank, more than $2,000c. Loan from the dealer, less than $2,000d. Bank, less than $2,000e. EquivalentAnswer: cIn terms of FV, $15,000 vs $14,000*(1.12)^1=$15,680. You can save $680 in terms of FV by getting a zero rate loan the dealer.4. Susie Orman argues that you can have more money by saving $100 each month (starting at the end of this month for 12 deposits) instead of saving $1,200 at the end of each year. To check whether that is true, you are going to compare saving $600 every six months for a year (starting from 6 months from today for 2 deposits) vis-à-vis $1,200 at the end of the year. What is the future value of $600 saved every six months for a year at the end of the first year at 10% APR?a. $1,100b. $1,135c. $1,230d. $1,740e. $1,200Answer: cSusie’s argument: better to save less and more frequently than to save more and less frequently. 600*(1.05)+600=$1,230, FV of $1,200 saved at the end of the year=$1,200, FV of $1,200 you save today= 1,200*(1.05)^2=1,323 (Aside: 10% with no 6 month compounding = 1,200*1.1=1,3205. How long does it take to triple your investment at 6% per year? a. 7.2 yearsb. 10.2 yearsc. 12.9 yearsd. 14.6 yearse. 18.9 yearsAnswer: eI=6, PV=-1, FV=3 => N=18.85, 18.9 years6. Which of followings is NOT the characteristics of a perpetuity?a. A perpetuity continues for a fixed time period.b. Value of a perpetuity can be calculated as “PMT/i”c. In a perpetuity, returns are earned in the form of a series of cash flows.d. A perpetuity is a constant infinite stream of identical cash flows.e. Real estate and preferred stock are effectively perpetuities.Answer: a7. If an investment of $87,250 is earning 5% interest rate compounded annually, how long will it take for this investment to reach a value of $99,750 if no additional withdrawals or no deposits are being made during the period?a. 2.47 yearsb. 2.52 yearsc. 2.74 yearsd. 2.61 yearse. 2.83 yearsAnswer: cPV = -87,250, I = 5, FV = 99,750 ⇨ N = 2.74 years8. If a security of $17,200 is worth $20,390 three years in the future and assuming that no withdrawals or deposits are made, what is the implied interest rate that the investor expects to earn on the security?a. 4.19%b. 5.84%c. 6.78%d. 7.82%e. 8.24%Answer: bN = 3, PV = -17,200, FV = 20,390 ⇨ I = 5.8%9. Keanu’s financial planner suggested once he crosses a threshold of $4,991,331 in savings, he will have enough money for retirement. Keanu has nothing saved for his retirement yet, so he has to start depositing $85,000 in retirement fund at a fixed rate of 12.00% at the end of each year. How long will it take for Keanu to retire?a. 15.64 yearsb. 18.40 yearsc. 23.00 yearsd. 24.84 yearse. Keanu will not be able to retireAnswer: bI = 12, PMT = 85,000, FV = 4,991,331 ⇨ N = 18.40 years10. You’ve decided to buy a house that is valued at $1 million. You have $500,000 as a down payment on the house and you take out a mortgage for the rest. Your bank is offering you a 30-year standard mortgage at a fixed nominal rate of 9% or a 15-year mortgage at a fixed nominal rate of 9%. How much larger must your monthly payment would be?a. $1,048.22b. $1,205.45c. $1,519.92d. $1,729.56e. $1,836.69Answer: a30-year: N = 360, I = 9/12, PV = 500,000 ⇨ PMT = $4,023.1115-year: N = 180, I = 9/12, PV = 500,000 ⇨ PMT = $5,071.33Therefore, difference is $1,048.2211. You’ve decided to buy a house that is valued at $1 million. You have $500,000 as a down payment on the house and you take out a mortgage for the rest. Your bank is offering you a 30-year standard mortgage at a fixed nominal rate of 9% or a 15-year mortgage at a fixed nominal rate of 9%. How much more interest will you pay if you took out a 30-year mortgage instead of a 15-year mortgage?f. $535,480.20g. $631,866.64h. $685,414.66i. $738,962.68j. $876,543.21Answer: a30-year: N = 360, I = 9/12, PV = 500,000 ⇨ PMT = $4,023.11Total payments = $4,023.11 * 360 = $1,448,319.6, Principal = $500,000 ⇨ Interest = $948,319.615-year: N = 180, I = 9/12, PV = 500,000 ⇨ PMT = $5,071.33Total payments = $5,071.33 * 180 = $912,839.4, Principal = $500,000 ⇨ Interest = $412,839.4Therefore, difference is $535,480.2012. How long will it take for you to pay off $1,000 charged on your credit card, if you plan to make the minimum payment of $15 per month and the credit card charges 24% per annum? a. 10 yearsb. 12 yearsc. 15 yearsd. 17 yearse. You may not be able to pay off the debtAnswer: eIf you use a financial calculator, you may get an error message because $15 of monthly payment is too small to pay back $1,000 at 24% per annum. In other words, it takes almost forever to pay back $1,000 at 24% per annum with monthly payment of $15.13. Which of the following investments would have the lowest present value? Assume that the effective annualrate for all investments is the same and is greater than zero.a. Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments).b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).d. Investment D pays $2,500 at the end of 10 years (just one payment).e. Investment E pays $250 at
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