FIN3320 HW Questions Exam 1
You are considering a car loan with a stated APR of 6% based on monthly compounding. What is the effective annual rate of this loan?
EAR = (1+APR/#of periods)^#of periods - 1 (1+.06/12)^12 - 1 = 6.167%
16. You have $100,000 to donate to your college. You want to endow a perpetual scholarship that makes its first payment in 1 year. If the college's discount rate is 4%, how large will the annual scholarship payment be?
PV = C/r PV=$100,000 r = 5% C = $4000
17. If you still donate the $100,000 from Problem 16 today, but ask the college to delay the scholarship payment so that the first scholarship payment is made 10 years from today, then how large will the annual payment be?
$5693.25
20. You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $2356 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have just made your monthly payment. The mortgage interest rate is 6.375% (APR). How much do you owe on the mortgage today?
30 yrs - 4 yrs & 8 months (360 months - 56 months) = 304 months remaining APR / Annual Percent Rate = 6.375% / 12 = .53125% Plug into excel PV(.0053125, 304, -2356) PV = $2356 (1/.0053125 - 1/.0053125(1.0053125)^304) = $354899.99
21. . You have just sold your house for $1,000,000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly 18½ years old, and you have just made a payment. If the interest rate on the mortgage is 5.25% (APR), how much cash will you have from the sale once you pay off the mortgage?
360 yrs - 18.5 yrs = 138 months remaining Find monthly payment PV = 800,000*.004375(1/.004375(1.004375)^360) = $4417.63 PV = $4417.63 (1/.004375 - 1/.004375(1.004375)^138) = $456,931.45 $1,000,000 - $456,932.45 = $543,069
30. Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has $3996 in it and pays an 8% interest rate. a. How much money would be in the account if you left the money there until your 25th birthday? b. What if you left the money until your 65th birthday? c. How much money did your grandfather originally put in the account?
FV = PV(1+r)^n a. 3996*1.08^7 = $6848.44 b. 3996*1.08^47 = $148,779.44 c. 3996/1.08^18 = $999.99 ($1,000)
19. If your bank pays you 1.5% interest and you deposit $500 today, what will your balance be in 5 years?
FV = PV(1+r)^n $500 x 1.015^5 = $538.64
26. Your cousin is currently 12 years old. She will be going to college in 6 years. Your aunt and uncle 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 4% per year, how much money do they need to put into the account today to ensure that they will have $100,000 in 6 years?
FV = PV(1+r)^n 100,000/1.04^6 = $79,031.45
18. You are considering a savings bond that will pay $100 in 10 years. If the interest rate is 2%, what should you pay today for the bond?
FV = PV(1+r)^n 100/1.02^10 = $82.03
20. Assume that your parents wanted to have $160,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 8% per year on their investments. a. How much would they have to save each year to reach their goal? b. If they think you will take five years instead of four to graduate and decide to have $200,000 saved just in case, how much more would they have to save each year to reach their new goal?
FV of Annuity = PMT x (1+r)^n - 1 / r FV = $160,000 n = 18 8% interest 160,000 x .08 = PMT (1.08^18) -1) = $4272.34 FV = $200,000 200,000 x .08 = PMT (1.08^18) -1) = $5340.42 or 4272.33/ x = 160,000/200,000 a. $4272.34 b. $5340.42
You plan on saving $4,000 a year for retirement and expect to retire in 40 years. You also expect an inheritance of $50,000 in 15 years which you will be able to add to your retirement savings. How much will you be able to spend annually from your retirement savings, if you expect to live for 30 years after you retire? Assume no taxes and an interest rate of 5%. All numbers are in nominal value.
Find FV of the $4,000 $4,000 x (1.05^40 -1)/.05 = $483,199.1 Calculate FV of inheritance $50,000 x (1.05^25) = $169,317.75 Add both = $652,516.85 Calculate cash flow PV of Annuity for after retirement CF(1/r-1/r(1+r)^n) $652,516.85= withdrawal amount * (1-1/1.05^30/.05) = $42477.29
21. When you purchased your car, you took out a five-year annual-payment loan with an interest rate of 6% per year. The annual payment on the car is $5000. You have just made a payment and have now decided to pay off the loan by repaying the outstanding balance. What is the payoff amount for the following scenarios? a. You have owned the car for one year (so there are four years left on the loan)? b. You have owned the car for four years (so there is one year left on the loan)?
PV = PMT(1/r - 1/r(1+r)^n) (4 years left) PV = $5000(1/.06 - 1/.06(1.06)^4) = $17325.53 or 5000/.06 (1 - 1/1.06^4) (1 year left) PV = $5000(1/.06 - 1/.06(1.06)) = $4716.98 a. $17325.53 b. $4716.98
10. You have a loan outstanding. It requires making three annual payments of $1000 each at the end of the next three years. Your bank has offered to allow you to skip making the next two payments in lieu of making one large payment at the end of the loan's term 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 to the two forms of payment?
Plug into FV calculator n=3 pmt = $1000 interest rate = 5% PV = $2,723.25
You are looking to buy a car and you have been offered a loan with an APR of 6%, compounded monthly. a. What is the true monthly rate of interest? b. What is the EAR?
True monthly rate of interest .06/12 = .005 .05% EAR (1+.06/12)^12 - 1 = 6.167%
20. Consider the following alternatives: i. $100 received in one year ii. $200 received in 5 years iii. $300 received in 10 years a. Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year. b. What is your ranking if the interest rate is only 5% per year? c. What is your ranking if the interest rate is 20% per year?
a. $100 - 1 year 100/1.1 = $90.9 (3) 200/1.1^5 = $124.18 (1) 300/1.1^10 = $115.66 (2) b. r = 5% 100/1.05 = $95.24 (3) 200/1.05^5 = $156.71 (2) 300/1.05^10 = $184.17 (1) c. r = 20% 100/1.2 = $83.33 (1) 200/1.2^5 = $80.38 (2) 300/1.2^10 = $48.45 (3)
17. Suppose the interest rate is 4%. a. Having $200 today is equivalent to having what amount in one year? b. Having $200 in one year is equivalent to having what amount today? c. Which would you prefer, $200 today or $200 in one year? Does your answer depend on when you need the money? Why or why not?
a. FV = C*(1+r)^n 200 x 1.04 = 208 b. PV = C / (1+r)^n 200 / 1.04 = 192.31 c. Having $200 today is preferred since its value decreases overtime. Investing money now would result in more than $200 in one year.
12. A friend asks to borrow $55 from you and in return will pay you $58 in one year. If your bank is offering a 6% interest rate on deposits and loans: a. How much would you have in one year if you deposited the $55 instead? b. How much money could you borrow today if you pay the bank $58 in one year? c. Should you loan the money to your friend or deposit it in the bank?
a. FV=PV * (1+r) 55 x 1.06= 58.3 b. PV=FV/1+r 58/1.06= $54.72 c. Depositing money in the bank will give you more money
8. You have just received a windfall from an investment you made in a friend's business. She will be paying you $10,000 at the end of this year, $20,000 at the end of next 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. Find NPV $10,000/1.035 = $9661.84 $20,000/1.035^2 = $18,670.21 $30,000/1.035^3 = $27,058.28 $9661.84+$18,670.21+$27,058.28 = $55,390.33 b. $10,000 x 1.035 = $10,350 + $20,000 = $30,350 x 1.035 = $31,412.25 + $30,000 = $61,412.25