Simple Annuities Due are annuities where payments are made at the beginning of. each period and the compounding period is EQUAL to the payment period (P/Y = C/Y) The formula for determining the present value of an annuity is PV = dollar amount of an individual annuity payment multiplied by P = PMT * [1 – [ (1 / 1+r)^n] / r] where: ... PMT = Dollar amount of each payment. r = Discount or interest rate. n = Number of periods in which payments will be made.
P=PMT • 1-(1/(1+r)^n)/r
Example: most car leases are simple annuities due, where payments are made monthly and interest rates are compounded monthly.
A general annuity is an annuity where the payments do not coincide with the interest periods. You will be able to see that it is very easy to deal with general annuities once an equivalent interest rate is determined with that equivalent rate being compounded as often as the payments are made. A = 1(1 + i)2 ** n = 2, the number of times interest is compounded per year. Now find the amount of the annuity using the annuity formula. ... Here the payment interval( 1 year ) is different than the interest period ( ¼ year). This is a general annuity.
Example: Monthly payments of $500 where interest is 6%/a, compounded monthly. Here the payment interval and the interest interval are the same – 1 month.
A deferred annuity is an insurance contract that guarantees retirement income at a future date. Deferred annuities differ from immediate annuities in that income payments are delayed until the date specified in the insurance contract. Earnings on the premium grow tax-deferred until the money is withdrawn. The formula of deferred annuity is P = Annuity Payment · r = Rate of Interest · n = Number of Periodic Payments · t = Period of Delay.
Example: Someone who is 50 years old might purchase a deferred annuity with the intention of receiving income at the age of 65 or even at 80. The greater the length of time between your annuity purchase and the payout, the more time the value will have to potentially grow.
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