Annuity Due a sequence of equal payments that are made at the beginning of the period...

Present Value of Annuity Due

 the present value of an annuity due, or its value on the day of the first payments, is the sum of the present values of the payments of the payments.

Formula for Present Value of Annuity Due:

Sample Problem:

Mr. Abad invested P1000 per month for 5 years at 9% compounded monthly. What is the cash equivalent of the 5-year deposits?

Amount of Annuity DueThe amount of an annuity due or its value at the end of the term is the sum of the accumulated values of the payments at the end of the term.

Formula for the Amount of Annuity Due:

Sample Problem:An investment of P200 is made at the beginning of each year for 10 years. If interest is worth 6%, how much will the investment be worth at the end of 10 years?

Periodic Payments of Annuity Due

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Sample Problem:The beneficiary of a life insurance policy may take P10000 cash or 10 equal annual payments, the first is to be made immediately. What is the annual payments if money is worth 6%?

Periodic Payments of Annuity Due

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Sample Problem:A student wants to have P2500 for a trip after graduation 4 years from now. How much she invest at the beginning of each year starting now if she gets 5% compounded annually on her savings?

Finding the n:

If..A=P10000i=6%R=P1281.7n?

If..S=P2500i=.05R=P552.41n?

Rate of Annuity Due

n-1 i =a

n+1 i =s

Sample Problem:

Instead of paying P9000 rental at the beginning of each month for the next 7 ½ years, Mr. Red decides to buy a small lot in the province. If the cash equivalent of the lot is P30819, what is the rate compounded monthly?

Deferred Annuity

Is one in which the first payment is made not at the beginning or end of the first period, but at some later date.

Formula to be used:

Sample Problem:Find the present value of a deferred annuity of P500 a year for ten years that is deferred 5 years. Money is worth 6%.

Sample Problem:Find S(def):If:R=P300d=6 yearsn=8i=7%