Deferred Annuity and Perpetuity: Financial Mathematics Concepts and Applications, Summaries of Engineering

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ANNUITY

(part 2)

Engr. Jordan Ronquillo

OBJECTIVES:

• Define Deferred Annuity and Perpetuity
• Compute for the Present worth and Future worth
• Solve problems involving Deferred Annuity and Perpetuity

Deferred Annuity Present amount of Deferred annuity, P

𝐀

𝐀

−𝐀 Where: i = interest per period k = deferral period n = number of periods A = uniform payment 𝐀+𝐀 𝐀 −𝐀 𝐀+𝐀 𝐀 𝐀 = uniform series present worth factor

PROBLEMS

1. A man loan Php 187,400 from a bank with interest at 5% compounded annually. He agrees to pay his obligations by paying 8 equal annual payments, the first being due at the end of 10 yrs. Find the annual payments. Ans: A = Php 44,982.
2. A house and lot can be acquired by a downpayment of Php 500,000 and a yearly payment of Php 100,000 at the end of each year for a period of 10 years, starting at the end of 5 years from the date of purchase. If money is worth 14% compounded annually, what is the cash price of the property? Ans: Php 808,835.

PROBLEMS

3. A boy is entitled to a 10 yearly endowments of Php 30,000 each starting at the end of the eleventh year from now. Using an interest rate of 8% compounded annually, what is the value of these endowment now? Ans: Php 93,
4. A man invested Php 100,000 every end of the year for 10 years, then waited for another 10 years for his money to grow. If his investment earned 8% after tax, compounded annually, what would be the sum of his investments and earnings at the end of the 20th year. Ans: Php 3,127,

Perpetuity

Perpetuity is an annuity that does not have a fixed time span but

continues indefinitely.

There is no definite future in perpetuity, thus, there is no formula for

the future amount.

Perpetuity

Solution

P1 and P2 https://youtu.be/OtASYz8fung

Thank You