Annuity: Definition, Types, and Applications, Summaries of Engineering

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ANNUITY

Engr. Jordan Ronquillo

OBJECTIVES:

• Define annuity, present worth and future worth
• Differentiate the type of annuity
• Identify how compound interest is related to annuity
• Solve problems on different types of annuity

Types of Annuity

1. Ordinary Annuity

2. Annuity Due

3. Deferred Annuity

4. Perpetuity

Ordinary Annuity

It is a type of annuity where the payments are made at the end

of each period beginning from the first period.

Ordinary Annuity Future amount of ordinary annuity, F

𝐀

Where: i = interest per period n = number of periods A = uniform payment 𝐀+𝐀 𝐀 −𝐀 𝐀 = uniform series compound amount factor

Ordinary Annuity Present amount of ordinary annuity, P

𝐀

𝐀

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

Annuity Due

P = A

1 − 1 +𝐀 1 −𝐀 𝐀

F = A

1 +𝐀 𝐀+ 1 − 1 𝐀

Where:

P = present amount

F = Future amount

i = interest rate

A = annuity

n = no. of interest periods

(𝐀𭰀𝐀𴰀𝐀𝐀𝐀 𝐀𪀀𝐀𳠀𝐀𝐀 𝐀𴀀 𝐀𝐀𝐀𳠀𝐀𝐀𝐀 𝐀𳠀𝐀 𝐀𳠀𝐀𳠀𭰀𝐀 𝐀𪀀𝐀𳠀𝐀𝐀 𝐀𴀀 𝐀𝐀𝐀𳠀𝐀𝐀𝐀 𝐀𳠀𝐀

PROBLEMS

1. What is the present worth of a 3 years annuity paying Php 3,000 at the end of each year, with interest at 8% compounded annually? Given: A = Php 3, i = 8% = 0. n = 3 yrs Required: P, present worth

PROBLEMS

2. Mr. Ricardo Dalisay purchased on monthly installment a Php 100,000 worth of land. The interest rate is 12% nominal and payable in 20 years. What is the monthly amortization? Given: P = Php 100, i = 12% (Monthly) = 0.12/12 = 0. n = (20 x 12) = 240 periods Required: A, monthly amortizations

Solution: 𝐀 =

𝐀 − 𝐀 𝐀 + 𝐀 𝐀 𝐀 𝐀𝐀𝐀, 𝐀𝐀𝐀 =

𝐀􄀀𝐀 − 𝐀 𝐀 + 𝐀. 𝐀𝐀 𝐀􄀀𝐀 𝐀. 𝐀𝐀 A = Php 𝐀, 𝐀𝐀𝐀. 𝐀􃠀 ans

Solution: 𝐀 =

𝐀 − 𝐀 𝐀 𝐀 =

􃰀 − 𝐀 𝐀. 𝐀􃰀 𝐀 = Php 􄀀𝐀, 􄀀􃰀􄀀. 𝐀􃠀 ans

PROBLEMS

4. A person borrowed Php 500,000 at an interest rate of 18% compounded monthly. Monthly payments of Php 12,968.31 are agreed upon. The length of the loan in months closest to: Given: P = Php 500, A = Php 12,968. i = 18% (monthly) = 0.18/12 = 0. Required: n, No. of periods

ANNUITY DUE

PROBLEMS

1. Mr. Ayala borrows Php 100,000 at 10% annual interest. He must pay back the loan over 30 years with uniform monthly payment due on the first day of each month. What does Mr. Ayala pay each month. Given: P = Php 100, n = (30 x 12) = 360 periods i = 10% (monthly) = 0.10/12 = 0. Required: A, monthly payments