Present Value And Period Of Deferral Of A Deferred Annuity (Part 1)

Deferred Annuity

an annuity that does not begin until a given time interval has passed. It is a kind of annuity in which payments (or deposits) start in more than one period from the present. The first payment interval does not coincide with the first interest period and is put off to a later date.

Period of Deferral

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

Deferred Payment

a payment arrangement where payments start at a later date.

Artificial Payments

assumed payments during the period of deferral used to determine the present value of a deferred annuity.

Present Value of a Deferred Annuity

the present value of all actual payments after considering the deferral period.

To Determine Present Value of Deferred Annuity

find the present value of all k + n payments (including the artificial payments), then subtract the present value of all artificial payments.

R

present payment.

j

interest rate per period.

n

number of actual payments.

k

number of conversion periods in the deferral or number of artificial payments.

m

number of conversion periods per year.

r

nominal interest rate.

i

interest rate per period.

t

number of years or term.

Number of Artificial Payments (k)

calculated as the number of payments assumed during the deferral period.

Number of Actual Payments (n)

calculated as the total number of payments after the deferral period.

Period of Deferral Identification

can be determined by counting the number of artificial payments or skip payments.

Skip Payments

payments that would have occurred during the deferral period but are not actually paid.

Semi-annual Payment

payment made twice a year.

Quarterly Payment

payment made four times a year.

Monthly Payment

payment made once a month.