Finance Chapter 9
Calculate the present value of an annuity of £1 for 10 years if the interest rate per year is 10%.
£1[1/.1-1/(.1(1.1)^10)] = £6.14.
You have a piece of real estate for sale for $10,000. You are offered $1,295.05 per year for 10 years. What is the present value of this offer with an interest rate of 5%? Multiple choice question.
$10,000 Reason: N = 10 I/Y = 5% PMT = $1,295.05 FV = $0 (assumed) CPT PV = $10,000 Therefore, this is a fair offer.
You have won a small lottery of $1,000,000. However, instead of a lump sum amount, the lottery will pay you $50,000 per year for 20 years (total of $1,000,000). If interest is 4%, what is the present value of your winnings, assuming payments are received at the end of each year? (Note: Ignore inflation and taxes)
$679,516 Reason: N = 20 I/Y = 4% PMT = $50,000/yr FV = $0 (assumed) CPT PV = $679,516
interest forumla
(FV/PV)^I/N-1
excel FV fuction
(rate, nper, pmt, [pv], [type]) rate- interest rate per period nper- total number of periods pmt- payment made each period for annunity pv- prsent value type- optional argument that can be omitted for this problem
annuity
A series of consecutive payments or receipts of equal amounts.
annuity due
A series of consecutive payments or receipts of equal amounts., come at the beginning of each period
annuity equaling future value formula
A= FVa/ [ (1+i)^n - 1 / i]
annuity equaling present value formula
A= PVa/ [1- 1/ (1=i)^n / i]
Which of the following is a deferred annuity? Multiple choice question. First payment begins at the beginning of year 3. First payment begins at the end of year 1. First payment begins at the beginning of year 1.
First payment begins at the beginning of year 3.
which keys on calculator represent the number of periods and the interest rate as described in each of the prior equations
N and I/Y BUT some calculators use I rather than I/Y
what excel fuction calculates the number of periods
NPER (rate, pmt, pv, [fv], [type])
intrest rate on excel
NPER(rate, pmt, pv, [fv], [type])
What key is used for annuity problems
PMT
PV OR FV value on excel
PMT(Rate, nper, pv, [fv], [type])
True or false: For a simple annuity, the value of n means the total number of payments which coincides with the total number of compounding periods.
True Reason: For a simple annuity, the payment interval and the compounding frequency match. Therefore, the the total number of payments coincides with the total number of compounding periods.
how to calculate number of periods on calculator
enter 10 fuction I/Y Enter 1000 fuction PV Enter -1464.1 fuction FV Enter 0 fuction PMT Fuction CPT Fuction PV Solution 4
present value of annuity on calculator
enter 20 fuction N Enter 2 fuction I/Y Enter 0 fuction PV Enter -2000 fuction PMT Fuction CPT Fuction PV Solution 32,702.87
PV on calculator
enter 4 fuction N ENTER 10 Fuction I/Y Enter -1464.1 fuction FV Enter 0 fuction PMT Fuction CPT Fuction PV Solution 1000.0
interest rate on calculator
enter 4 fuction N Enter -3169.87 Fuction PV Enter 1000 Fuction PMT Enter 0 Fuction FV Fuction CPT Fuction I/Y Solution 10.00
future value of annuity of calculator
enter 4 fuction N Enter 10 fuction I/Y Enter -1000 fuction PMT Enter 0 fuction PV Fuction CPT Fuction PV Solution 4,641
annuity payment on calculator
enter 4 fuction N Enter 10 fuction I/Y Enter -3169.87 fuction PV Enter 0 fuction FV Fuction CPT Fuction PMT Solution 1,000.00
present value of annuity on calculator
enter 4 fuction N Enter 10 fuction Y/Y Enter 0 fuction FV Enterre-1000 fuction PMT Fuction CPT Fuction PV Solution 3169.87
Interest value on calculator
enter 4 fuction N Enter 1000 fuction PV Enter -1464.1 fuction FV Enter 0 fuction PMT Fuction CPT Fuction PV Solution 10
annuity payments are what size and occur when
equal size and occur at end of each year
pv formula
fv [1/(1+i)^n]
Which of the following are the correct number of periods (n) and interest rate (i) per period to use to calculate the present value of a 12% loan that requires quarterly payments of $1,000 over 5 years? (Check all that apply.)
i= 3 n=20
deferred annuity
if annunity will be paid at some time in the future
An increase in the interest rate will: Multiple select question.
increase the future value decrease the present value
A decrease in the interest rate Blank______ the present value of a single sum to be received in the future
increases Reason: The PV represents the amount one would have to pay today to receive a specific lump sum in the future. If the interest rate is lower then the initial investment (PV) required will be higher because it will earn less interest over time.
arguments
inputs on excel
the future value assumes amount is invested when and grows when
invested at beginning of the period and grows to the end of the period
Number of periods formula
ln (FV/PV) / ln (1+i)
the financial calculator does not require us to use the __ fuction
log
The number of periods (n) and interest rate (i) per period used in calculating the present value of an annuity that is paid monthly over 5 years at 12% annually are Blank______.
n=60 i=1 The number of periods is the total number of interest payments which is 60 (=12 payments per year times 5 years). The interest is the interest rate per payment which is 1% (=12% per year divided by 12 payments per year).
what type= 0 means on excel
ordinary annuity
interest rate on excel
rate(nper,pmt,pv,[fv], [type], [guess])
Number markers are at
the end of each year but also mark the beginning of the next year
In solving a general annuity problem, the interest rate that should be used is Multiple choice question.
the equivalent periodic rate per payment period. Reason: In solving a general annuity problem, the equivalent periodic rate per payment period, i2 = (1 + i)c − 1, should be used.
Calculator assumes either PV or FV is a cash outflow so the solution will have
the opposite sign EX. because a negative value was entered for PV the final solution will be positive
how to determine how much interest is paid overtime
total payments - repayment of principal= payments applied to interest
compounding semiannually
A compounding period of every six months. For example, a five-year investment in which interest is compounded semiannually would indicate an n value equal to 10 and an i value at one-half the annual rate.
ordinary annuity
A payment stream with payments that occur at the end of each year.
How to clear TVM memory
2ND CLR TVM
how to clear regular memory of calculator
2nd CLR WORK
How to set decimal place on calculator
2nd FORMAT 4 Enter
If an investment of $2,000 pays 10% interest, how many periods will it take for the investment to have a value of $2,662?
3 Reason: I/Y = 10% PV = -$2,000 PMT = $0 (assumed) FV = $2,662 CPT N = 3.0 periods
FV ad formula
A X ( (1+i)^n+1 - 1 / i -1)
PVad formula
A X ( 1- 1/(1+i)^n-1 / i + 1)
how to clear the screen of calculator
CE/C CE/C
clear cash flow values on calculator
CF 2nd CLR WORK
Future value on calculator
Enter 10 fuction N Enter 4 fuction I/Y Enter -1000 fuction PV Enter 0 fuction pmt fuction cpt fuction FV solution 1,480.24
how to enter on a calculator the future value of 1,000 if it is invested at 10 percent and compounds for 4 years
Enter 4 Fuction N Enter 10 Fuction I/Y Enter -1000 Fuction PV Enter 0 Fuction PMT Fuction CPT FUCTION PV Solution 1464.10
other algebraic formulas for pv
FV (1/(1+I))/^N FV/(1+I)^N FV(1+I)^-N
excel fuction for future value of annuity
FV(Rate, nper, pmt,[pv], [type])
5 basic functions of excel
FV, PV, RATE, NPER, PMT
Future Value Formula
FV=PV(1+I)^n
Future value of annuity formula
FVa=A[ (1+i)^n-1/ i ] FVa- future value of annuity A-Annuity payment i- interest rate n- number of payments
Present value on excel
PV(rate, nper, pmt, [fv], [type])
present value annuity formula
PVa= A X (1- 1/ (1+i)^n / i)
what Excel fuction calculates interest rate
RATE (NPER, PMT, PV, [FV],[TYPE], [GUESS])
$1,000 invested today will be worth $1,330 three years from today. What is the interest rate? Round to the nearest whole percentage.
Reason: N = 3 PV = -$1,000 PMT = $0 (assumed) FV = $1,330 CPT I/Y = 9.97% =>10%
future value of annuity assumes amount is invested when and grows to
end of period and grows to end of next period
present value
The current or discounted value of a future sum or annuity. The value is discounted back at a given interest rate for a specified time period.
Which of the following is true regarding a deferred annuity? Multiple choice question.
The period of deferral can end on either the date of the first payment or one payment interval prior to the first payment in the annuity.
discount rate
The rate at which future sums or annuities are discounted back to the present.
future value of annuity
The sum of the future value of a series of consecutive equal payments.
present value annuity
The sum of the present value of a series of consecutive equal payments.
Future Value Definition
The value that a current amount grows to at a given interest rate over a given time period.
number of payments on calculator
enter 10 fuction I/Y Enter -3169.87 fuction PV Enterr 1000 Fuction PMT Enter 0 fuction FV Fuction CPT Fuction I/Y Solution 4.00
what type=1 means on excel
annuity due
ordinary annuity
annuity payments are to come at the end of each payment period
An increase in the number of periods will Blank______ the present value of a single sum.
decrease Reason: The PV represents the amount one would have to pay today to receive a specific lump sum in the future. If the number of compounding periods is higher then the initial investment (PV) required will be lower because it will earn more interest over the extra periods.
compounding
earning more interest on a previous period's interest
