FIN640-C6
What is the difference in the future value of $100 at 7% interest for 5 years if the interest is compounded semiannually rather than annually?
$0.80
Use a financial calculator to compute the present value of $100 per year for 30 years if the discount rate is 5%?
$1,537.25
Find the future value of an annuity of 100 per year for 10 years at 10 percent per year.
$100x[1.10 10th - 1]/.10 = $1,593.74
Which of the following are real-world examples of annuities?
-pensions -mortgages
If the stated interest rate is 10 percent, what is the EAR if interest is compounded monthly?
10.47%
What is the present value of an ordinary annuity that pays $100 per year for three years if the interest rate is 10 percent per year?
=248.69
Most investments involve:
Multiple cash flows
One example of a perpetuity is a British ____.
consol
You have decided to fund an account that will pay your descendants the inflation-adjusted equivalent of $100 per year forever. You assume inflation will equal 3% per year, and you expect the account to earn 7% per year. How much do you need to put in the account today to ensure your gift will continue forever?
$2,500
Use your financial calculator to find the future value of an annuity of $400 per year for 10 years at 5%.
$5,031.16
Suppose you paid a $1,200 loan off by paying $400 in principal each year plus 10% yearly interest. How much is the second interest payment?
$80 You are re-paying $400 each year. Interest is computed on the principal outstanding for the year, which is ($1,200 - 400) = 800. $800 x 0.1 = $80
$100 at the end of each year forever at 10% per year is worth how much today?
100/.1=1000
At the end of 5 days, you repay your $1,000 loan plus $50 in interest. What is the EAR?
3,422.24%
You owe $1,200 on your credit card, which charges 1.5% per month. If you pay $50 per month starting at the end of this month, how many months will it take to pay off your credit card?
30 months
Which of the following is the simplest form of loan?
A pure discount loan
Which compounding interval will result in the lowest future value assuming everything else is held constant?
Annual
An annuity due is a series of payments that are made _____.
At the beginning of each period
Which of the following is the formula for future value of an annuity?
The formula for the future value of an ordinary annuity is F = P * ([1 + I]^N - 1 )/I
You are considering an investment that will earn the following cash flows over the next three years. You expect to earn 6% return on the investment. Match each cash flow with its present value, then match the total amount you should pay for the investment today to the appropriate box. Year 1: $5,000 Year 2: $6,000 Year 3: $5,500
Year 1: $4,716.98(5000/1.06) Year 2: $5,339.98(6000/1.06^2) Year 3: $4,617.91(5500/1.06^3) Amount you should pay for the investment: $14.674.87
A lump sum payment to pay off the balance of a partially amortized loan is called a ____ payment.
ballon or bullet
Payday loans allow you to ____/
borrow now and repay later
Assume interest is compounded monthly. The ______ annual rate will express this rate as though it were compounded annually?
effective
What type of amortization is most commonly used in the real world for mortgages and car loans?
fixed playment
If the interest rate is greater than zero, the value of an annuity due is always ___ an ordinary annuity.
greater than
For a positive stated annual interest rate and multiple compounding periods per year, the EAR is always _____ the APR.
larger than
Compared to a comparable fixed payment loan, the total interest on a fixed principal loan is ___.
less
A traditional (non-growing) annuity consists of a(n) _________ stream of cash flows for a fixed period of time
level
A single cash flow is also known as a :
lump sum
The loan balance on partial amortization loans declines so slowly because the _____.
payments are mostly interest.
The present value formula for a(n) ___________ is PV=C/r, where C is the constant and regularly timed cash flow to infinity, and r is the interest rate.
perpetuity
The formula for the ____________ value interest factor of an annuity is {1 - [1/(1 + r)^t]/r}
present
Amortization is the process of paying off loans by regularly reducing the _________
principal
The original loan amount is called the:
principal
With interest-only loans that are not perpetuities, the entire principal is:
repaid at some point in the future
Because of _____________ and ____________, interest rates are often quoted in many different ways.
tradition; legislation
semi-annual compounding means that interest is paid _________ per year.
two-times
Which of the following are true about the amortization of a fixed payment loan?
-the amount of interest paid decreases each period -the principal amount paid increases each period
In the Excel setup of a loan amortization problem, which of the following occurs?
-the payment is found using PMT (rate, nper, -pv, fv) -to find the principal payment each month, you subtract the interest payment from the total payment.
If the interest rate is 10 percent per week, what is the EAR? ( Please note that 10 percent per week is not an APR. It is a weekly rate (Quoted rate/m)). Assume 52 weeks in a year.
14104%
The difference between the present value of an ordinary annuity with payments of $100 per year at 10% compounded annually for 10 years
1a)PV of ordinary annuity = PMT*(1-(1+r)-n)/r = 100*(1-(1+10%)-10)/10% = 614.46PV of ordinary annuity due = (1+r)*PMT*(1-(1+r)-n)/r = (1+10%)*100*(1-(1+10%)-10)/10% = 675.90Difference = 675.90-614.46 = 61.45
An APR of 9% with continuous compounding gives an EAR of:
9.42%
The present value interest factor for an annuity with an interest rate of 8 percent per year over 20 years is _____.
9.8181
You agree to pay back $1100 in 4 weeks for a $1000 payday loan. Your annual percentage rate APR rounded to two decimal places is _____%assume weekly compounding and 52 weeks in the year.
=(1100/1000-1)*52/4 =130%
The general formula for the ____ is (1+r/m)^m -1.
EAR
An effective annual rate of 7.12 percent is equal to 7 percent compounded _________.
Semiannually
APR
The interest rate per period multiplied by the number of periods in the year. EAR
EAR
The interest rate stand as though it were compounded once per year.
You expect to receive bonuses with your job at the end of each year for the next five years. Assume you can invest all of your bonuses at 4.5%, and the bonuses are as shown below, match each amount to its future value at the end of the five years, then match the total to the appropriate box. Year 1: $500 Year 2: $1,200 Year 3: $1,000 Year 4: $2,400 Year 5: $2,200
Year 1: $596.26 Year 2: $1,369.40 Year 3: $1,092.03 Year 4: $2,508.00 Year 5: $2,200.00 Total after 5 years: $7,765.68
When calculating the present value of multiple cash flows using a spreadsheet, you must:
calculate the present value of each cash flow and then add the discounted values together
In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the ______________ of each period.
end
How frequently does continuous compounding occur?
every instant
The formula for the present value of an annuity due is:
(1 + r) x (PV of an ordinary annuity)
Ralph has $1,000 in an account that pays 10 percent per year. Ralph wants to give this money to his favorite charity by making three equal donations at the end of the next 3 years. How much will Ralph give to the charity each year?
$402.11
Which of the following is true about a growing annuity?
- The cash flows grow at a constant rate. - The cash flows grow for a finite period.
What are two ways to calculate a balloon payment?
-Amortize the loan over the loan life to find the ending balance -Find the present value of the payments remaining after the loan term
Suppose you need $5,000 in one year, $4,3000 in two years, and $5,000 in three years. Match each present value amount to the corresponding cash flow assuming a discount rate of 17%. 1. Present Value of the Year 1 Cash Flow 2. Present Value of the Year 2 Cash Flow 3. Present Value of the Year 3 Cash Flow
1. $4,273.50($5,000/1.17) 2. $3,314.21($4,300/1.17^2) 3. $3,121.85($5,000/1.17^3)
a 5 year $10,000 loan with 15 year amortization period paid monthly at 10 percent compounded monthly will have monthly payments of
107.46... 1000 / (1- (1/(.1/12)^12x15)/(.1/12))
To find the present value of an annuity of $100 per year for 5 years at 10 percent per year using the tables, look up the present value interest factor which is ______ and multiply that by ______.
3.7908; $100 Number of periods on the table = 5, interest rate of 10% = 3.7908 Present value interest value = $100
Amy took out a mortgage of $100,000 at 4.5% with monthly payments for 30 years. What is her payment to principal and interest each month?
506.69
Which of the following spreadsheet (Excel) functions will calculate the $614.46 present value of an ordinary annuity of $100 per year for 10 years at 10% per year?
=PV(0.10,10,-100,0,0)
If C=$100, g=10%, r=15%, and t=2 years, then what is the PV of this growing annuity?
PV = 100 x [1 - (1.1/1.15)^2 ] // .15 - .1 = 100 x 1.701323 = $170.13
You will receive a bonus of $5000 in one year and would like to take a loan against it now. How much can you borrow if you plan to use the entire amount to pay back the loan and your interest rate is 3%?
PV=500/(1.03)^1=4854.37
Another common name for the effective annual rate is the annual percentage ____.
yield
Which of the following processes can be used to calculate future value for multiple cash flows?
- Calculate the future value of each cash flow first and then add them up - Compound the accumulated balance forward one year at a time
Which of the following are ways to amortize a loan?
- Pay principle and interest every period in a fixed payment. - Pay the interest each period plus some fixed amount of principle.
Which of the following should be valued using a perpetuity formula?
- Preferred stock - Cash flows from a product whose sales are expected to remain constant forever - A console (bond that pays interest only and does not mature)
Which of the following are true about a partial amortization loan?
-The amortization period is longer than the loan period -The monthly payments do not fully pay off the loan by the end of the loan period -The borrower makes a large balloon payment at the end of the loan period. -The monthly payment is based on a longer amortization period than the maturity of the loan.
Given the same APR, more frequent compounding results in:
higher EARs