The present value of $1.00 is computed by dividing $1.00 by the amount of $1.00 at the given rate for the given number of periods, as shown in the table.

Illustration. What is the present value of $1.00 due in two years, interest at 6% per annum compounded semi-annually?

SOLUTION. The amount of $1.00 for 4 periods at 3% (see table) is $1.125509. Then $1.00 1.125509 = $.888487 Present value of $1.00 Example. What is the present value of $1,500.00 due in two years, interest at 6% per annum, compounded semi-annually?

The accumulation of interest by which $1,322.72 increases to $1,500.00 may be tabulated as follows:

239. Compound Discount. The compound discount on $1.00 is the difference between $1.00 and the present value of $1.00.

Illustration. What is the compound discount on $1.00 due in two years, interest at 6% per annum, compounded semi-annually?

SOLUTION.

Deduct present value of $1.00 (as above)
Compound discount

1.000000

.888487

.111513

Written Work

1. State the total amount accumulated at the end of five years, and the compound interest earned, on $5,000.00 invested at

(a) 6% per annum, compounded annually.

(b) 6% per annum, compounded semi-annually.
(c) 6% per annum, compounded quarterly.

2. What is the present value of $5,000.00 due at the end of five years,

(a) at 6% per annum, compounded annually?
(b) at 6% per annum, compounded semi-annually?
(c) at 6% per annum, compounded quarterly?

CHAPTER XXVI

CONTRACT PURCHASES AND INSTALLMENT PAYMENTS

REAL estate, furniture, musical instruments, automobiles, and other forms of property are often sold on installments due at monthly or other intervals. The contract usually specifies definite amounts which must be paid, and permits the debtor to pay larger amounts. The purchaser also pays interest on the principal.

240. Long End Interest is interest on the balance of the principal unpaid between the dates of successive installments. The contract may require:

(a) An equal periodical payment on the principal in addition to the long end interest. To illustrate:

On May 1, 1921, C purchased a piano from D for $1,200.00, paying $200.00 down. The balance was to be paid in monthly installments of $25.00. In addition, long end interest was to be paid monthly at the rate of 6% per annum. A record of the payments might be kept in the following manner:

(b) An equal periodical payment which shall be applied first to the payment of long end interest and the balance to principal, as follows:

241. Short End Interest is interest on the installment being paid, computed from the date of the purchase until the date of paying the installment. To illustrate, assume that in the preceding illustration C agrees to pay $25.00 monthly with short end interest at the rate of 6% per annum, as follows:

1. Mr. Adams buys a phonograph from Z on April 1, 1922, for $300.00 to be paid for in monthly installments with interest at 6%. Prepare a table showing the monthly payments if the installments are to be $25.00 plus long end interest.

2. Prepare a table showing the payments if the installments are to be $25.00 monthly, long end interest being deducted from the installments, the balance being applied on the principal.

3. Prepare a table showing the payments if the installments are $25.00 with short end interest.

4. Compare the total payments including principal and interest in the first three problems.

5. On May 1, 1921, G. A. Sanders sold a house and lot to A. R. Crain; purchase price, $4,850.00. Mr. Crain paid $2,900.00 cash and gave the following note for the balance.

CONTRACT PURCHASES AND INSTALLMENT PAYMENTS 279

$1,950.00

BARTLETT, IOWA, MAY 1, 1921

FOR VALUE RECEIVED, I promise to pay to the order of G. A. Sanders, the sum of Nineteen Hundred and Fifty Dollars, with interest thereon at the rate of six per cent per annum, principal and interest payable in monthly installments in the sum of twenty-five dollars or more, each, the first of which is due on June 1, 1921, and one on the first day of each and every month thereafter until said principal sum of Nineteen Hundred and Fifty Dollars and interest thereon are fully paid. Each and every of said installments is to be applied as follows:

1st. In payment of accrued interest on said sum of $1,950.00 or on the unpaid portion thereof.

2d. In monthly reduction of said principal sum of $1,950.00.

Notice that some payments are made on the second day of the month, due to the fact that the first day of the month was either Sunday or a holiday.

Prepare a statement showing a record of the payments made.

6. Assume that the contract between Mr. Sanders and Mr. Crain called for a monthly payment of $25.00 or more, and that the principal was to be decreased semi-annually by amounts computed as follows: The payments for six months shall be added and from their sum shall be deducted six months' interest on the balance of the principal unpaid at the beginning of the semi-annual period. Payments were made as indicated above. Prepare a statement showing the reduction of the debt.

7. Which of the two propositions is better for Mr. Crain? Explain why.