Finance Questions
What is the present value of $1000 (C) paid at the end of each of the next 100 years if the interest rate is 7% per year?
14,269.25 PV(annuity) = (C/r)(1-(1/((1+r)^N))) annuity problem
You are saving for retirement. To live comfortably, you decide you will need to save $2 million by thetime you are 65. Today is your 30th birthday, and you decide, starting today and continuing on everybirthday up to and including your 65th birthday, that you will put the same amount into a savingsaccount. If the interest rate is 5%, how much must you set aside each year to make sure that you willhave $2 million in the account on your 65th birthday?
20868.91 use C = P/((1/r)(1-(1/((1+r)^N)))) Find the PV of the FV and set equal to PV(annuity) = (C/r)(1-(1/((1+r)^N))) and solve for C
You have a loan outstanding. It requires making three annual payments at the end of the next three years of $1000 each. Your bank has offered to restructure the loan so that instead of making the three payments as originally agreed, you will make only one final payment at the end of the loan in three years. If the interest rate on the loan is 5%, what final payment will the bank require you to make so that it is indifferent between the two forms of payment?
3152 Use Sum of Cn/((1+r)^n) for each individual cash flow to get present value of cash flows you would give and then use FV = PV(1+r)^n to get the future value of the previous thing
Your daughter is currently eight years old. You anticipate that she will be going to college in 10years. You would like to have $100,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3% per year, how much money do you need to put into the account today to ensure that you will have $100,000 in 10 years?
74,409.39 FV = PV(1+r)^n
You have found three investment choices for a one-year deposit: 10% APR compounded monthly 10% APR compounded annually, 9% APR compounded daily. Compute the EAR for each investment choice. (Assume that there are 365 days in the year.)
a) 10.471% b) 10% c) 9.416% Use the EAR/APR conversion formula or hit "2nd" and "2" on the calculator and enter/CPT your numbers and know "NOM" is "APR"
When you purchased your house, you took out a 30-year annual-payment mortgage with an interstate of 6% per year. The annual payment on the mortgage is $12,000. You have just made a payment and have now decided to pay the mortgage off by repaying the outstanding balance. What is the payoff amount if: a. You have lived in the house for 12 years (so there are 18 years left on the mortgage)? b. You have lived in the house for 20 years (so there are 10 years left on the mortgage)? c. You have lived in the house for 12 years (so there are 18 years left on the mortgage) and you decide to pay off the mortgage immediately before the twelfth payment is due?
a) 129,931.24 b) 88,321.04 c) 141,931.24 (the same but 12000 additional)
The British government has a consol bond outstanding paying £100 per year forever. Assume the current interest rate is 4% per year. a. What is the value of the bond immediately after a payment is made? b. What is the value of the bond immediately before a payment is made?
a) 2500 b) 2600 Use PV (of perpetuity cash flows) = PMT/r add + 100 to include the current payment for answer b
Calculate the future value of $2000 in: a. Five years at an interest rate of 5% per year. b. Ten years at an interest rate of 5% per year. c. Five years at an interest rate of 10% per year.
a) 2522,56 b) 3257.79 c) 3221.02 FV = PV(1+r)^n *expect to find present value given future instead*
You have just made an offer on a new home and are seeking a mortgage. You need to borrow $600,000. a. The bank offers a 30-year mortgage with fixed monthly payments and an interest rate of 0.5% per month. What is the amount of your monthly payment if you take this loan? b. Alternatively, you can get a 15-year mortgage with fixed monthly payments and an interest rate of 0.4% per month. How much would your monthly payments be if you take this loan instead?
a) 3597.30 b) 4682.49 use C = P/((1/r)(1-(1/((1+r)^N))))
Oppenheimer Bank is offering a 30-year mortgage with an EAR of 5 If you plan to borrow $150,000, what will your monthly payment be?
From EAR, find discount rate and use the loan annuity formula (with N = 360) to solve for monthly payments 828.02
You are considering moving your money to a new bank offering a one-year CD that pays an 8% APR with monthly compounding. Your current bank's manager offers to match the rate you have been offered. The account at your current bank would pay interest every six months. How much interest will you need to earn every six months to match the CD?
Need to convert APR to EAR, then do discount rate of EAR With 8% APR, we can calculate the EAR as follows: EAR = (1+(0.08/12))^12 = 8.3% Over six months this works out to be 1.083^(1/2) - 1 = 0.040672. Hence you need to earn 4.0672% interest rate to match the CD.
You are shopping for a car and read the following advertisement in the newspaper: "Own a new Spitfire! No money down. Four annual payments of just $10,000." You have shopped around and know that you can buy a Spitfire for cash for $32,500. What is the interest rate the dealer is advertising (what is the IRR of the loan in the advertisement)? Assume that you must make the annual payments at the end of each year.
The PV of the car payments is a four-year annuity: Setting the NPV of the cash flow stream equal to zero and solving for r gives the IRR: 32500 = (10000/r)(1-(1/((1+r)^4))) To find r, we either need to guess or use the annuity calculator. You can check and see that r = 8.85581% solves this equation. So the IRR is 8.86%.i
You make monthly payments on your mortgage. It has a quoted APR of 5% (monthly compounding). What percentage of the outstanding principal do you pay in interest each month?
discount rate = 0.41667% the discount rate is derived from EAR, which is derived from APR
You have just received a windfall from an investment you made in a friend's business. He will be paying you $10,000 at the end of this year, $20,000 at the end of the following year, and $30,000 at the end of the year after that (three years from today). The interest rate is 3.5% per year. a. What is the present value of your windfall?b. What is the future value of your windfall in three years (on the date of the last payment)?
a) 55,390 b) 61,142 a) Cash flow = Sum of Cn/((1+r)^n) for each individual cash flow b) use FV = PV(1+r)^n On calculator, click "CF" and input appropriate cash flows for all "C"s, and put "1" for "FOs". At the end, click "NPV" and put in the interest rate for "I" and enter. Then, "CPT" on "NPV"
Your bank is offering you an account that will pay 20% interest in total for a two-year deposit. Determine the equivalent discount rate for a period length of a. Six months. b. One year. c.One month
a) knowing that six months is 1/4 of 2 years, using formula (1+0.2)^(1/4) = 1.0466 so 4.66% b) 9.54% c) 0.763%
