Chap 2: Time Value of Money

Meaning of time value of money

Money available at the present time is worth more than the same amount in the future.

Money can earn interest or be invested to generate returns over time. Therefore, the value of money changes over time .

formula of future value

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FV = PV x (1 + r)^n

where r is the interest rate and n is the number of compounding periods.

Effective Annual Rate (EAR or EFF)

The actual annual interest rate that takes into account the effect of compounding.

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The EAR is important for comparing different investment options that have different compounding periods.

The formula for EAR

EAR = (1 + (APR / m))^m - 1

where m is the number of compounding periods in a year.

The formula for calculating the Annual Percentage Rate (APR) is:

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APR = \[(2 x Monthly Interest Rate x Number of Months) / (Number of Months + 1)\] x 100

Annual Percentage Rate

The interest rate charged on a loan or credit card on an annual basis, including any fees or additional costs associated with the loan.

formula of nominal rate

The formula for nominal rate is:

Nominal Rate = Real Rate + Inflation Rate

what is discounting

Discounting is the process of determining the present value of a future payment at discount rate

what is annuities

A stream of equal cash flow

Ordinary annuity

Start at the end of the current period

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Example of an ordinary annuity is a car loan where the borrower makes equal monthly payments to the lender for a fixed number of months.

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Another example is a retirement plan where an individual contributes a fixed amount of money to the plan at the end of each year for a certain number of years.

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Immediate annuity/ Annuity due

Start at the beginning of each period

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a lease payment, where the renter pays the landlord at the beginning of each month trả tiền thuê nhà đầu tháng

Growth Perpetuity

Growth overtime, accumulate funds over time

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An example of a growth annuity would be a retirement savings plan, where an individual contributes a fixed amount of money each year and earns a fixed rate of return on their investment. Over time, the contributions and interest earned accumulate to provide a larger retirement fund.

Money is

anything that is generally accepted in payment for goods and services or in the repayment of debt

Currency includes

paper money and coins

The total collection of pieces of property that serve to store value is a personʹs

wealth

Income

is a flow of earnings per unit of time