hree local government units in Metro Manila have agreed to pool their resources from taxes for the construction of a major road connecting their areas. It is estimated that an amount of P500,000 is to be deposited at the end of the year into a shared account for the first phase of the project which will last 9 years after the initial deposit has been made. The deposit will increase by P100,000 per year after the initial deposit up until the lifetime of the project. Assume 5% annual interest rate. Determine: (a) Total present worth of the deposits (b) Construct the equivalent cash flow diagram
hree local government units in Metro Manila have agreed to pool their resources from taxes for the construction of a major road connecting their areas. It is estimated that an amount of P500,000 is to be deposited at the end of the year into a shared account for the first phase of the project which will last 9 years after the initial deposit has been made. The deposit will increase by P100,000 per year after the initial deposit up until the lifetime of the project. Assume 5% annual interest rate. Determine: (a) Total present worth of the deposits (b) Construct the equivalent cash flow diagram
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
Topic: Gradients
General Direction: Solve using Given-Required-Solution format. DO NOT USE EXCEL. Provide a Cash Flow Diagram (CFD). Use the formula given.
Three local government units in Metro Manila have agreed to pool their resources from taxes for the construction of a major road connecting their areas. It is estimated that an amount of P500,000 is to be deposited at the end of the year into a shared account for the first phase of the
project which will last 9 years after the initial deposit has been made. The deposit will increase by P100,000 per year after the initial deposit up until the lifetime of the project. Assume 5% annual interest rate. Determine:
(a) Total present worth of the deposits
(b) Construct the equivalent cash flow diagram
![Uniform Arithmetic Gradient
Key words: increase or decrease by a uniform amount each period
Ascending arithmetic progression
P = PA + PG
G[(1+ i)" – 1
PG
i
1
i
|(1+ i)"|
[1-(1+i)¯
PA = A
i
Geometric Gradient
Key words: increase / decrease by percentage
Instead of fixed value
P = A[1 - (1+ g/1+i)"]
i-g
where: P= Present of all cash flow between periods 1 and n
A = Cash flow in period 1
g= rate of change per period
i= effective interest rate per period](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F663a8350-ddb2-49bd-9368-86cbfa00f5e3%2F0aaa9b36-51bc-41f5-9e08-92e7157a1f86%2Fqtbkcjd_processed.png&w=3840&q=75)
Transcribed Image Text:Uniform Arithmetic Gradient
Key words: increase or decrease by a uniform amount each period
Ascending arithmetic progression
P = PA + PG
G[(1+ i)" – 1
PG
i
1
i
|(1+ i)"|
[1-(1+i)¯
PA = A
i
Geometric Gradient
Key words: increase / decrease by percentage
Instead of fixed value
P = A[1 - (1+ g/1+i)"]
i-g
where: P= Present of all cash flow between periods 1 and n
A = Cash flow in period 1
g= rate of change per period
i= effective interest rate per period
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