ANNUITY
Engr. Jordan Ronquillo
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Annuity: Definition, Types, and Applications, Summaries of Engineering
Geology in Engineering xmvlknvev
Typology: Summaries
2022/2023
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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𝐀𝐀𝐀𝐀 𝐀𪀀𝐀𝐀𝐀 𝐀 𝐀𝐀𝐀𝐀𝐀𝐀 𝐀𝐀 𝐀𝐀𭰀𝐀 𝐀𪀀𝐀𝐀𝐀 𝐀 𝐀𝐀𝐀𝐀𝐀𝐀 𝐀𝐀
PROBLEMS
- 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
- 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 =
𝐀𝐀 − 𝐀 𝐀 + 𝐀. 𝐀𝐀 𝐀𝐀 𝐀. 𝐀𝐀 A = Php 𝐀, 𝐀𝐀𝐀. 𝐀 ans
Solution: 𝐀 =
𝐀 − 𝐀 𝐀 𝐀 =
− 𝐀 𝐀. 𝐀 𝐀 = Php 𝐀, . 𝐀 ans
PROBLEMS
- 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
- 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