ANNUITIES

Question 1

is a sequence of payments made at equal (fixed) intervals or periods of time

Answer 1

ANNUITY

Question 2

insurances, social security system or investments that are long term are examples of what

Answer 2

ANNUITY

Question 3

an annuity “pay-out” may be ______ or ______.

Answer 3

immediate or deferred

Question 4

an annuity may be classified into the following

Answer 4

ACCORDING TO:
PAYMENT INTERVAL AND INTEREST PERIOD
TIME OF PAYMENT
DURATION

Question 5

TYPES OF ANNUITY ACCORDING TO:

PAYMENT INTERVAL AND INTEREST PERIOD

Answer 5

SIMPLE ANNUITY

GENERAL ANNUITY

Question 6

TYPES OF ANNUITY ACCORDING TO:

TIME OF PAYMENT

Answer 6

ORDINARY ANNUITY

ANNUITY DUE

Question 7

TYPES OF ANNUITY ACCORDING TO:

DURATION

Answer 7

ANNUITY CERTAIN

CONTINGENT ANNUITY

Question 8

type of annuity where payment interval is the same as the interest period

Answer 8

SIMPLE ANNUITY

Question 9

type of annuity where payment interval is not the same as the interest period

Answer 9

GENERAL ANNUITY

Question 10

type of annuity where payments are made at the end of each payment interval (Annuity Immediate)

Answer 10

ORDINARY ANNUITY

Question 11

type of annuity where payments are made at the beginning of each payment interval

Answer 11

ANNUITY DUE

Question 12

type of annuity where payments begin and end at a definite period

Answer 12

ANNUITY CERTAIN

Question 13

type of annuity where payments extend over an indefinite or indeterminate length of time

Answer 13

CONTINGENT ANNUITY

Question 14

time between the first payment interval and the last payment interval

Answer 14

Term of an Annuity (t)

Question 15

the amount of each individual payment

Answer 15

Regular or Periodic payment (R)

Question 16

sum of future values of all payments to be made during the entire term of an annuity

Answer 16

Future Value of an Annuity (F)

Question 17

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)

Answer 17

Present Value of an Annuity (P)

Question 18

formula for the future value of a simple ordinary annuity

Answer 18

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)

Question 19

formula for the present value of a simple ordinary annuity

Answer 19

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)

Question 20

CASH PRICE is the sum of the ___________ and the ________________

Answer 20

down payment; and

present value of the installment payments

Question 21

formula for R if FUTURE value is given for simple ordinary annuity

Answer 21

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)

Question 22

formula for R if PRESENT value is given for simple ordinary annuity

Answer 22

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)

Question 23

method of paying a loan (principal and interest) on installment basis, usually of equal amounts at regular intervals

Answer 23

amortization

Question 24

formula for computing for the equivalent rate r in general annuity

Answer 24

(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

Question 25

an annuity that does not begin until a given time interval has passed

Answer 25

DEFERRED ANNUITY

Question 26

payments in deferred annuity are done at some _____ period of time

Answer 26

later

Question 27

is the time between the purchase of an annuity and the start of the payments for the deferred annuity

Answer 27

PERIOD OF DEFERRAL

Question 28

R* is called ____________ where each are equal to R but are not actually paid during the period of deferral

Answer 28

ARTIFICIAL PAYMENTS

Question 29

to compute for the Present Value of a deferred annuity, simply subtract the _______________ from the ________________

Answer 29

present value of all artificial payments;

present value of payments made during the (k+n) period

Question 30

formula for the present value of deferred annuity

Answer 30

P = (R(1+j)^-k)((1 - (1+j)^-n)/j)
where:
k is the period of deferral

Question 31

identify the period of deferral in this deferred annuity:

Monthly payments of P50,000 for three years that will start 8 months from now

Answer 31

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

Question 32

identify the period of deferral in this deferred annuity:

Annual payments of P2,500 for 24 years that will start 12 years from now.

Answer 32

k = 11, n=24

Question 33

identify the period of deferral in this deferred annuity:

Quarterly payments of P300 for 9 years that will start a year from now

Answer 33

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

Question 34

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

Answer 34

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