Present Worth of Annuities

make equal payments

payments of #

period per timeinterest

paymentregular

n

i

R

i

iRA

n

n)1(1

The present value of an annuity that pays out n regular payments of $R at the end of each time period from an account with an interest rate of i per time period is:

(plus interest)Future worth of annuity (lump sum)

withdraw equal amounts

(while earning interest)

Present worth of annuity (lump sum)

Example 1

From a settlement, you will be awarded $1000 at the end of every month for the next 30 years paid from an annuity earning interest at an annual rate of 6%. What amount must be in the account to achieve this goal?

i

iRA

n

n)1(1

1000360

10003

10002

1000_________1

end withint bbmonth

00.0

Annuity DuePresent Value of Annuity Due – when the payouts occur at the beginning of each time period.

)1()1(1

)1(duen, ii

iRiAA

n

n

Example 2$1,260,000 Jackpot winner gets a choice of:a) $3500/month for 30 years paid at the beginning of each month with 7.5% annual rateb) Lump sum of the present value

Tom and Alice inherit $100,000 and put this into an annuity paying out at the start of each month for 5 years with interest of 6.3%, compounded monthly. How much will they receive each month?

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)1(duen, ii

iRiAA

n

n

Example 3

If they get an annuity paying 7.2%, how long will the same payout last?