Handbook of Civil Engineering Calculations

FIGURE 1. Time, receipt, and payment diagram.

x = payment made on January 1 of year 5 and 1.5* = payment made on January 1 of year

6. Substituting, we get $900(1.338) + $1200(1.191) = $700(1.124) + 1.06 + 1.5; x =
   $721.30. Hence, 1.5* = $1081.95.
   Related Calculations: Note that this procedure can be used for more than two
   loans and for payments of any type that retire a debt.

ANALYSIS OFA NONUNIFORM SERIES

On January 1 of a certain year, ABC Corp. borrowed $1,450,000 for 12 years at 6 percent

interest. The terms of the loan obliged the firm to establish a sinking ftind in which the

following deposits were to be made: $200,000 at the end of the second to the sixth years;

$250,000 at the end of the seventh to the eleventh years; and one for the balance of the

loan at the end of the twelfth year. The interest rate earned by the sinking fund was 3 per-

cent. Adverse financial conditions prevented the firm from making the deposit of

$200,000 at the end of the fifth year. What was the amount of the final deposit?

Calculation Procedure:

1. Prepare a money-time diagram
   Figure 2 shows a money-time diagram for this situation, where * = deposit made at end of
   twelfth year.


2. Compute the principal of the loan at the end of the twelfth year
   Use the relation S = P(SPCA) for i = 6 percent, n = 12. Obtain the SPCA value from an
   interest table, and substitute in the above relation, or S= $1,450,000(2.012) = $2,917,400.

Payments

Receipts

Valuation

date

All sums (except x) in units of $1000

FIGURE 2. Money-time diagram.

Year