Calculation Procedure:
Compute the interest earned by $1 per year
With four interest periods per year, the interest rate per period = / = 6 percent/4 =1.5 per-
cent. In 1 year there are four interest periods for this account.
Find the compounded value of $1 at the end of 1 year from S = (1 + i)
n
= (1 + 0.015)
4
= $1.06136. Thus, the interest earned by $1 in 1 year = $106136 - 1.00,000 = $0.06136.
Hence, the effective interest rate = 6.136 percent.
PERPETUITY DETERMINATION
What sum must be deposited to provide annual payments of $10,000 that are to continue
indefinitely if the endowment fund earns interest of 4 percent compounded semiannually?
Calculation Procedure:
- Compute the effective interest rate
Using the same procedure as in the previous calculation procedure for $1, we find the ef-
fective interest rate ie = (1.02)^2 - 1 = 0.04040, or 4.04 percent. - Apply the USPW relation
The endowment or principal required = P = payment//e, or P = $10,000/0.0404 =
$247,525.
DETERMINATION OF EQUIVALENT SUMS
Jones Corp. borrowed $900 from Brown Corp. on January 1 of year 1 and $1200 on Janu-
ary 1 of year 3. Jones Corp. made a partial payment of $700 on January 1 of year 4. It was
agreed that the balance of the loan would be discharged by two payments, one on January
1 of year 5 and the other on January 1 of year 6, with the second payment being 50 per-
cent larger than the first. If the interest rate is 6 percent, what is the amount of each pay-
ment?
Calculation Procedure:
- Construct a line diagram indicating the loan data
Figure 1 shows the line diagram for these loans and is typical of the diagrams that can be
prepared for any similar set of loans. - Select a convenient date for evaluating all the sums
For this situation, select January 1 of year 6. Mark the valuation date on Fig. 1, as shown. - Evaluate each sum at the date selected
Use the applicable interest rate, 6 percent, and the equivalence equation, value of money
borrowed = value of money paid. Substituting the applicable SPCA factor from the inter-
est table for each of the interest periods involved, orw = 5,« = 3,w = 2, and n — 1, respec-
tively, gives $900(SPCA) + $1200(SPCA) = $700(SPCA) + jc(SPCA) + 1.5*, where