For each problem, you need toshow your work in order to receive credit. A correct answerwith no work shown gets half credit (which means you fail the assignment). Anincorrect answer with no work receives 0 credit. With time value of money (TVM)problems, that means showing your inputs for the financial calculator. Make yourfinal answer very clear for the graders. Please don’t make them hunt for youranswer.It would make sense to the work like the steps you input into a Texas Instruments BA-II Plus Adv Financial CalculatorForexample, on 1a, I would show:N =x; I/Y = x; PV = x; PMT = 0, Compute FV = _______Foruneven cash flows, show CF0 = xx, CF1 = xx F01 = x; CF2 = xx F02 = x, etc. I/Y = xx, Compute PV _____Showall dollar and percentage values to two decimals($xxx.xx) and percentage values to x.xx% (be sure to have enough decimalsshowing on your calculator). Rounded answers will receive point deductions.Dono interim rounding on interest rates. For example, ifthe interest rate is 4.7% with monthly compounding, enter 4.7 then the dividekey, then 12, and the “=” key, then hit the I/Y key. That would be 4.7/12 = 0.39166….Your calculator will probably show 0.3917 (assuming you are showing 4 decimals,or 0.39 if you only show 2 decimals). If you have followed my instructions,your calculator is holding the complete value, but only showing the number ofdecimals you have the calculator set to.Insome cases, an equation will be easier than using the TVM keys, show yourequation if that is the case.Ifyou use Excel, show what the equation and inputs used.Aswith all TVM problems, assume annual compounding unless otherwise specified.If you are given and interest rate, assume it is the annual percentage rate(APR).1.(a) If you deposit $13,500 in the bank today, what isits future value at the end of twenty years if it is invested in anaccount paying 4.20% interest (annual compounding, which is the same asAPR)?(b) What is the present value of $13,500 to be received in twentyyears if the appropriate interest rate is 4.20% APR?2.We sometimes need to find how long it will take a sumof money (or anything else) to grow to some specified amount. Note that youshould enter PV as a negative and FV as a positive.(a) For example, if a company’s sales are growing at a rateof 4.20% per year, approximately how long will it take sales to triple?Show your answer to 2 decimals (x.xx years). If you are not sure how to workthis, go back to this week’s practice problems.(b) If you want an investment to double in twenty years,what interest rate must it earn? Show your answer to 2 decimals (x.xx%). Donot approximate using the “rule of “72”.3.(a) You aresaving for retirement, and you can afford to save $18,000 every year, startingone year from today. If you invest for 30 years at an annual interest rate of 5.25%per year, how much will you have saved for your retirement? Hint, this isthe FV of an annuity. You may want to solve parts (c) and (e), then come backand solve (b) and (d), which are annuities due.(b) How much would you have in your retirementaccount if you began these same 30 annual payments immediately? Hint: Thisis now the FV of an annuity due.c) Now let’s look at things a little differently. Supposethat once you retire, you want to be able to withdraw $80,000 per year(starting one year from your retirement) for a total of 25 years during yourretirement. How much would you need to have in your account when you retire tomake this work assuming an annual interest rate of 5.25%? Hint: This is thePV of an annuity.(d) How much would you need to have in your retirementaccount if you began these same 25 annual withdrawals immediately?Hint:This is now the PV of an annuity due. Reset your calculator to “END” of periodpayments when you have finished the annuity due problems.(e) Changing the scenario, now let’s assume that you want tohave $1.8 million in your retirement account at the end of 30 years. You havenow decided that you will deposit funds at the end of every month for 30years. The interest rate is still 5.25% per yar. How much do you need todeposit each month in order to reach your goal in 30 years.?4.Compare the results you got in part a) for future valueof a “regular” annuity compare these to the value you got for theannuity due (part b). Now look compare the PV of the regular annuity in part (c)to the PV of an annuity due in part (d). What is the relationship that you see?Using the time value of money concepts you have learned so far, why does thisrelationship (FV of regular annuity vs. annuity due and PV of regular annuityvs. annuity due) occur? (4 points)5.You and your family have had a rough couple of yearsand are ready for a break. You feel you REALLY need a vacation. However, youhaven’t been able to save much over the past couple of years so you are lookingat vacation loan options. These are personal loans, sometimes even availablewhen you book your trip. You don’t have $5000 you need for the trip availableon your credit card, so you decide to go for the vacation loan.a) Your credit score isn’thorrible, but it isn’t great either. The best deal you can get is to pay a4.58% “origination fee” for the loan, which means that you are financing$5,240 but will only receive $5,000 for the trip. You set up a payment plan topay this $5,240 loan off over 4 years, with monthlypayments. The best interest rate that was offered to you was 15% (APR). 1)How much are your monthly payments and 2)how much in total are you reallypaying for this trip now? (I’m just looking for the sum of the payments made.)Up to 1 point for each answer.b) Discuss at least onealternative to the above scenario that gives your family a break, but withoutthe high cost of the vacation loan. FYI: I did a very quick Google search andfound quick ideas. I’m not looking for a lot here, just a few sentences andsome thoughts that will give your family a break without breaking the bank.Obviously, there is no single “correct answer” I’m looking for, justsome creative thinking.6.What is the present value of the following uneven cashflow stream? The appropriate interest rate is 15.50%, compounded annually. Notethat the final cash flow represents a project where there may be reclamation orother “end of project” costs which are greater than any final income and/orsalvage value. Note that the final cash flow represents a project wherethere may be reclamation or other “end of project” costs which are greater thanany final income and/or salvage value.7. What annual interest ratewill cause $13,500 to grow to $22,500 in twenty years (assume annualcompounding)? Show your answer to 2 decimals (x.xx%)8.Will the future value be larger or smaller if wecompound an initial amount more often than annually—for example, every 3 months(quarterly) — holding the stated interest rate constant? Explain your answer. Zerocredit unless there is an explanation.9 a) What is the future value of $13,500 (depositedtoday, no other deposits made) after twenty years under 4.20% annualrate, with semi-annual compounding?b) What is the effective annual rate (EAR) for 4.20% annualinterest, with interest compounded on a semiannual basis? Be sure toshow your EAR answer to 2 decimals, that is xx.xx%c) What is the future value of $13,500 (as above) after twentyyears under 4.20% annual rate, with quarterly compounding?d) What is the effective annual rate (EAR) for 4.20% annual interestrate with quarterly compounding?e) Explain how theeffective annual rate changes based on the number of compounding periods peryear.f) What is the future value of $13,500 (as above) after twentyyears under 4.20% annual interest, with daily compounding? Assume a 365-dayyear and do not do any interim rounding.g) What is the effective annual rate for 4.20% (APR)annual interest with daily compounding?10. Will the effective annualrate ever be equal to the simple (quoted) rate? Explain.11. Three years ago you bought ahome with a purchase price of $240,000 and you are paid 15% of that amount as adown payment and financed the remainder. Your mortgage loan terms are 30years of monthly payments at an annual rate of 4.50%. Do nointerim rounding on the calculated monthly interest rate.(a) How much are your monthlymortgage payments?(b) Over the life of the loan, how much did youpay in interest?(c) Remember that you took this loan out 3 yearsago (36 payments). Today, you feel that the value of your home has gone up anddecide that even though interest rates have increased, you want to refinance totake out equity to upgrade your kitchen. Considering the 3 years of paymentsyou have made; how much do you still owe on your home?12. (a) Assume that youwant to buy a new car and the interest rate you are offered is 9.36% APR(assuming a FICO credit score of only 590), with monthly payments for 4 years.You can afford a payment of $650 per month. What is the greatest amount you canborrow?(b) Now let’s assume that you decide that $650per month is more than you want to spend. In order to buy that same car (answerto part a), if you take your loan out over 6 years instead of only 4, how muchmore will you be paying in interest over the life of the loan compared to theprevious loan (part a)? Hint, you need to first calculate the alternatepayment, then your answer to this question is how much more in interest doyou pay over the life of the 6-year loan over the 4-year loan for the samevalue of car, with financing at the same interest rate?FYI: Seven years is the maximum term(currently) for auto loans, taking a longer loan will lower your monthlypayment (all things equal). Your decision is how much you can afford to pay andhow much more you are willing to pay in interest over the life of the loan. Forthis example, I am assuming that the interest rate doesn’t change.13. a) Suppose on January 1 youdeposit $13,500 in a savings account that pays a quoted interest rate of 2.40%(APR), with interest added (compounded) daily. How much will you have in youraccount on October 1, or after 9 months? (assume N = 273 days) Recall that theinterest rate (I/Y) represents the periodic rate based on how many times perYEAR the interest is compounded, hint, this is 365 times per year. Do nointerim rounding on the interest rate. As above, and for all TVM typeproblems, there should be no interim rounding of the interest rates.b) Now suppose you leave your money in the bank for 21months. Thus, on January 1 you deposit $13,500 in an account that pays a 2.40%(APR), compounded daily. How much will be in your account on October 1 the nextyear? (assume N = 638 days). Do no interim rounding on the interest rate. Dono interim rounding on the interest rate. Do no interim rounding on theinterest rate.
