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Chapter 3: Combining Factors

When using factors, it is important to remember the following:

The present worth is always located one period prior to the first uniform-series amount when using the P/A factor.

The future worth is always located in the same period as the last uniform-series amount when using the F/A factor.

The present worth of an arithmetic gradient will always be located two periods before the gradient starts.

The present worth is located one period prior to the first geometric gradient amount.

Most estimated cash flow series do not fit exactly the series for which the factors and equations were developed. Then, factors have to be combined in the calculations of present worth, future worth, uniform-series, etc. Following are some examples demonstrating the use of combined factors.

1. Ali plans to purchase a car for $10000. He also expects to pay $1000 per year for its maintenance when the warranty on the car expires after 2 years, i.e. maintenance starts in the 3rd year. If he plans to keep the car for 6 years after the warranty expires, how much money should he allocate for these expenses, i.e. what will be the present worth of the payments, if the interest rate is 8% per year?

PT=?

P2 = ? i = 8% per year

P = ?

0 1 2 3 4 5 6 7 8 years

A = 1000

10000

The present worth of the uniform-series amounts, i.e A, is at year 2 when using the P/A factor.

P2 = 1000.(P/A,8%,6)

Its present worth now,

P = P2.(P/F,8%,2) = 1000.(P/A,8%,6).(P/F,8%,2) = 3963.21

Total present worth, PT = 10000 + 3963.21 = 13963.21

2. Suppose $20000 is deposited into an account that pays interest at a rate of 7% per year. If 10 equal annual withdrawals are made from the account, with the first withdrawal occurring three years after the deposit, how...