ANNUITIES Flashcards
is a sequence of payments made at equal (fixed) intervals or periods of time
ANNUITY
insurances, social security system or investments that are long term are examples of what
ANNUITY
an annuity “pay-out” may be ______ or ______.
immediate or deferred
an annuity may be classified into the following
ACCORDING TO:
PAYMENT INTERVAL AND INTEREST PERIOD
TIME OF PAYMENT
DURATION
TYPES OF ANNUITY ACCORDING TO:
PAYMENT INTERVAL AND INTEREST PERIOD
SIMPLE ANNUITY
GENERAL ANNUITY
TYPES OF ANNUITY ACCORDING TO:
TIME OF PAYMENT
ORDINARY ANNUITY
ANNUITY DUE
TYPES OF ANNUITY ACCORDING TO:
DURATION
ANNUITY CERTAIN
CONTINGENT ANNUITY
type of annuity where payment interval is the same as the interest period
SIMPLE ANNUITY
type of annuity where payment interval is not the same as the interest period
GENERAL ANNUITY
type of annuity where payments are made at the end of each payment interval (Annuity Immediate)
ORDINARY ANNUITY
type of annuity where payments are made at the beginning of each payment interval
ANNUITY DUE
type of annuity where payments begin and end at a definite period
ANNUITY CERTAIN
type of annuity where payments extend over an indefinite or indeterminate length of time
CONTINGENT ANNUITY
time between the first payment interval and the last payment interval
Term of an Annuity (t)
the amount of each individual payment
Regular or Periodic payment (R)
sum of future values of all payments to be made during the entire term of an annuity
Future Value of an Annuity (F)
sum of all present values of all the payments to be made during the entire term of annuity
it can be taken as the amount to be paid or invested if the payment will be made at a single instance (or lump sum)
Present Value of an Annuity (P)
formula for the future value of a simple ordinary annuity
F = R ( ( (1 + j)^n - 1) / j ) where: R – Regular Payment j – interest period per conversion (𝑗 = (𝑖^𝑚)/𝑚) n – number of conversion period (𝑛 = 𝑚𝑡)
formula for the present value of a simple ordinary annuity
P = R ( ( 1 - (1 + j)^-n ) / j ) where: R – Regular Payment j – interest period per conversion (𝑗 = (𝑖^𝑚)/𝑚) n – number of conversion period (𝑛 = 𝑚𝑡)
CASH PRICE is the sum of the ___________ and the ________________
down payment; and
present value of the installment payments
formula for R if FUTURE value is given for simple ordinary annuity
R = (F(j)) / ((1 + j)^n - 1) where: F – future value j – interest period per conversion (𝑗 = (𝑖^𝑚)/𝑚) n – number of conversion period (𝑛 = 𝑚𝑡)
formula for R if PRESENT value is given for simple ordinary annuity
R = (P(j)) / (1 - (1 + j)^-n) where: P – present value j – interest period per conversion (𝑗 = (𝑖^𝑚)/𝑚) n – number of conversion period (𝑛 = 𝑚𝑡)
method of paying a loan (principal and interest) on installment basis, usually of equal amounts at regular intervals
amortization
formula for computing for the equivalent rate r in general annuity
(1 + (i^m)/m)^m = (1 + r/m*)^m* where: r – rate (𝑖^𝑚)/𝑚 – interest period per conversion m* – frequency of payment every year m – frequency of compounding per year
an annuity that does not begin until a given time interval has passed
DEFERRED ANNUITY
payments in deferred annuity are done at some _____ period of time
later
is the time between the purchase of an annuity and the start of the payments for the deferred annuity
PERIOD OF DEFERRAL
R* is called ____________ where each are equal to R but are not actually paid during the period of deferral
ARTIFICIAL PAYMENTS
to compute for the Present Value of a deferred annuity, simply subtract the _______________ from the ________________
present value of all artificial payments;
present value of payments made during the (k+n) period
formula for the present value of deferred annuity
P = (R(1+j)^-k)((1 - (1+j)^-n)/j)
where:
k is the period of deferral
identify the period of deferral in this deferred annuity:
Monthly payments of P50,000 for three years that will start 8 months from now
Payment will start at month 8. Therefore there are 7 artificial payments from now.
k is 7, n is 36 and total conversion period is (7+36)=43
identify the period of deferral in this deferred annuity:
Annual payments of P2,500 for 24 years that will start 12 years from now.
k = 11, n=24
identify the period of deferral in this deferred annuity:
Quarterly payments of P300 for 9 years that will start a year from now
There are 4 quarters in a year. Payment will happen at the end of the 4th quarter. Therefore there are 3 quarters of artificial payments.
k = 3
n = 9(4) = 36
identify the period of deferral in this deferred annuity:
Semi-annual payments of P6,000 for 13 years that will start 4 years from now
In 4 years, there are 8 semi annual periods. Payment will begin at the end of the 8th period. Therefore there are 7 semi-annual periods for the artificial payment.
k = 7
n = 13(2) = 26 payment periods
