18 Questions
An ordinary annuity is a series of equal payments occurring at __________ intervals of time
equal
Annuities are established for the purpose of payment of debt by a series of equal payments at equal time intervals, also known as __________
amortization
A capital recovery factor is used to accumulate a certain amount in the future by depositing equal amounts at equal time intervals; these amounts are called a __________
sinking fund
A loan at Php 100 at simple interest of 10% will become Php 150 after 5 years. The cash flow diagram on the view of the lender represents a positive cash flow or cash ________
inflow
An ordinary annuity is a series of uniform payments made at equal intervals of time. It can be seen in examples like regular deposits of a savings account or monthly home mortgage payments. This type of annuity is established for accumulating a certain amount in the future by depositing equal amounts at equal time intervals; these amounts are known as a __________
sinking fund
The quantity in brackets is called the “______ series present worth factor” and is designated by the functional symbol P/A, i%, n, read as “P given A at i percent in n interest periods”.
uniform
The equation A=P 𝑖 1 − 1+𝑖 −𝑛 represents the __________ factor.
capital recovery
Annuities are established for the purpose of being a substitute periodic payment for a future lump sum payment. This type of annuity is used to accumulate a certain amount in the future by depositing equal amounts at equal time intervals; these amounts are known as a __________
sinking fund
An ordinary annuity is one where the payments are made at the ________ of each period.
end
A=F 𝑖 1+𝑖 𝑛 −1 represents the ________ factor.
sinking fund
What are the present worth and the accumulated amount of a 13 year annuity paying Php10,000.00 at the ________ of each year, with interest at 13% compounded annually?
end
How much money will you invest today in order to ______ Php4,500.00 annually for 10 years if the interest rate is 9%?
withdraw
An ordinary annuity is one where the payments are made at the ______ of each period.
end
Future Worth formula for Ordinary Annuity: F = A (F/A, i%, n). The quantity in brackets is called the 'uniform series compound amount factor' and is designated by the functional symbol F/A, i%, n, read as 'F given A at i percent in n interest ______s'. The equation can be expressed as: F = A (F/A, i%, n).
period
Annuity Elements of Annuity: P – Present Worth of all periodic payments, F – Future Worth of all periodic payments after the last payment is made, A – a series of periodic equal amounts of money/periodic payments, n – number of interest periods/payments, i – interest rate per interest period, r – nominal interest rate, m – number of compounding per year, t – time in years.
uniform
The quantity in brackets in the Future Worth formula is called the 'uniform series ______ amount factor' and is designated by the functional symbol F/A, i%, n, read as 'F given A at i percent in n interest periods'.
compound
Types of Annuity: Ordinary Annuity. An ordinary annuity is one where the payments are made at the ______ of each period.
end
Types of Annuity: Ordinary Annuity. Future Worth ______ for Ordinary Annuity: F = A (F/A, i%, n). The quantity in brackets is called the 'uniform series compound amount factor' and is designated by the functional symbol F/A, i%, n, read as 'F given A at i percent in n interest periods'.
formula
Study Notes
Cash Flow Diagram
- A graphical representation of cash flows drawn on a time scale
- Used in economic analysis problems, similar to a free body diagram in mechanics problems
- Receipt (positive cash flow or cash inflow) and Disbursement (negative cash flow or cash outflow) are represented
Cash Flow Diagram Example
- A loan of Php 100 at a simple interest rate of 10% will become Php 150 after 5 years
- View of the lender and borrower are shown in the cash flow diagram
Annuity
- A series of equal payments made at equal intervals of time
- Examples: regular deposits in a savings account, monthly home mortgage payments, and monthly insurance and pension payments
- Established for:
- Paying debt through a series of equal payments at equal time intervals (amortization)
- Accumulating a certain amount in the future by depositing equal amounts at equal time intervals (sinking fund)
- Substituting periodic payments for a future lump sum payment
Annuity Formulae
- Present Worth: P = A/(1 + i)^n - 1 / i
- The quantity in brackets is called the "uniform series present worth factor" and is designated by P/A, i%, n
- Ordinary Annuity: A = P * (i / (1 - (1 + i)^(-n)))
- The quantity in brackets is called the "capital recovery factor" and is designated by A/P, i%, n
- Ordinary Annuity (Finding A when F is given): A = F * (i / ((1 + i)^n - 1))
- The quantity in brackets is called the "sinking fund factor" and is designated by A/F, i%, n
Annuity Elements
- P: Present Worth of all periodic payments
- F: Future Worth of all periodic payments after the last payment is made
- A: Series of periodic equal amounts of money/periodic payments
- n: Number of interest periods/payments
- i: Interest rate per interest period
- r: Nominal interest rate
- m: Number of compounding per year
- t: Time in years
Types of Annuity
- Ordinary Annuity: Payments are made at the end of each period
- Future Worth: F = A * ((1 + i)^n - 1) / i
- The quantity in brackets is called the "uniform series compound amount factor" and is designated by F/A, i%, n
Test your knowledge on present worth and annuity equations including uniform series present worth factor and ordinary annuity calculations. Practice solving for P and A in different scenarios.
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