Handbook of Civil Engineering Calculations

3. Set up an expression for the principal In the sinking fund at the
   end of the twelfth year
   From Fig. 2, principal = $200,000(USCA, n = S)(SPCA, n = 8) + $200,000(SPCA, n = 6)

• $250,000(USCA, n = S)(SPCA, n = 1) + x. With an interest rate of 3 percent, principal
  = $200,000(3.091)(1.267) + $200,000(1.194) + $250,000(5.309)(1.030) + x, or principal
  = $2,389,100+ jc.

4. Compute the final deposit
   Equate the principal in the sinking fund to the principal of the loan: $2,389,100 + x =
   $2,917,400. Thus, jc = $528,300.

UNIFORM SERIES WITH PAYMENT PERIOD

DIFFERENT FROM INTEREST PERIOD

Deposits of $2000 each were made in a fund earning interest at 4 percent per annum com-
pounded quarterly. The interval between deposits was 18 months. What was the balance
in the account immediately after the fifth deposit was made?

Calculation Procedure:

1. Compute the actual interest rate
   Replace the interest rate I 3 for the quarterly period with an equivalent rate / 18 for the 18-
   month period. Or, I 18 = (1 +1 3 )" - 1 = (1.01)^6 - 1 = 6.15 percent.


2. Compute the USCA value
   Apply the equation USCA = [(I + /)" - 1]/*, or USCA - [(1.0615)^5 - 1]/0.0615 = 5.654.


3. Compute the principal in the fund
   Use the relation S = /2(USCA) = $2000(5.654) = $11,308.

UNIFORM-GRADIENT SERIES: CONVERSION

TO UNIFORM SERIES

A loan was to be amortized by a group of six end-of-year payments forming an ascending
arithmetic progression. The initial payment was to be $5000, and the difference between
successive payments was to be $400, as shown in Fig. 3. But the loan was renegotiated to

FIGURE 3. Diagram showing changed payment plan.

Poyments under

original terms

Poyments under

new terms