# Topic 2 - Introduction To Financial Mathematics (Time Value Of Money)

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This article is a topic within the subject Business Finance.

## Required Reading

Essentials of Corporate Finance (2nd Australian and New Zealand edition), by Stephen A. Ross, Rowan Traylor, Ron Bird, Randolph W. Westerfield and Bradford D. Jordan, McGraw Hill Irwin, 2010., pp. 92-152.

## Time Value of Money

 A dollar received today is worth more than a dollar received in the future. This is because you can invest the dollar today to generate a return that gives you a total of more than \$1 in the future. Future Value refers to the amount of money an investment will grow to over some period of time at a given interest rate i.e. the cash value of an investment in the future.

FV = PV(1+i)^n where (1+i)^n is called the Future Value Interest Factor (FVIF) Example: If \$100 is invested for 4 years at 10% per annum, what is the FV? FV = PV (1.1)^4 = \$146.41

## Discounting

 Present Value is the current value of future cash flows discounted at the appropriate discount rate/factor. E.g. how much is \$1 next year worth? The amount that I would need now to receive the future value at time ‘t’, at a given interest rate, after ‘t’ periods e.g. receive \$1 next year is worth \$0.909 today. The present value of a cash flow which will pay off after ‘n’ periods in the future is the amount that, if it were invested today, would grow into that value after ‘n’ periods.

## Changing the Compounding Period

1. Required to alter the periodic interest rate --> (annual rate)/periods
2. Alter the number of periods --> number of years × number of periods

## Interest Rates

• Nominal - the denoted or annual percentage rate (quoted by institutions)
• Effective (EFF) - the equivalent annual rate, EFF = (1 + nominal/m)^m
• The interest rate that would generate the same FV if annual compounding had been used.
• E.g. if a credit card has a 18% APR & payments are monthly the EAR = 19.56%
• Periodic - the interest rate per period

## Annuities

 An annuity is a sequence of equal payments made at fixed times for a specified number of periods. There are several types.

### Deferred Annuity

This is when the 1st cash flow occurs after a time period that exceeds the time period between each subsequent cash flow. To calculate; discount the cash flows to the time period of the first cash flow.

### Perpetuity

This is an annuity that goes on making payments indefinitely. Present Value = Payments / Interest Rate

### Other

• Promissory Notes - the payment of \$10,000 in 90 days, whilst the interest rate is 7%, thus the PV = \$9830.33 = 10000/((1+(0.07×90)/365))
• Interest Only Loans - 3 year, 10%, interest only loan of \$1000.
• Amortised Loan - Repay part of the principle as time goes by. The flows of cash are an annuity.

## End

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