FDNBUSM 01 · Simple Interest and Discount
Cards
01A 120-day PHP 100,000 face-value note is discounted at 12% on a 360-day year. What annual simple rate measures the cost of the PHP 96,000 proceeds?
12.5%
Discount is PHP 4,000. Annualize against proceeds: 4,000/(96,000 × 120/360) = .125. The quoted 12% uses face value.
Slater_Ch16_424-447 Textbook.pdf; Slater_Ch17_448-471 Textbook.pdf; 1-1_SimpleInterest.pdf; 1-2_DiscountInterest.pdf02On the same 200 actual days at a positive annual rate, why is ordinary interest greater than exact interest?
It divides the same day count by 360 instead of 365.
The numerator and principal are unchanged. A smaller year denominator makes the fraction of a year larger.
Slater_Ch16_424-447 Textbook.pdf; Slater_Ch17_448-471 Textbook.pdf; 1-1_SimpleInterest.pdf; 1-2_DiscountInterest.pdf03A borrower needs PHP 76,000 proceeds from a 6-month note at 10% simple bank discount. What face value must be issued?
PHP 80,000
P = F(1 − dt), so F = 76,000/.95 = 80,000. The discount base is face value.
Slater_Ch16_424-447 Textbook.pdf; Slater_Ch17_448-471 Textbook.pdf; 1-1_SimpleInterest.pdf; 1-2_DiscountInterest.pdf04For 18 January to 6 August 2026, what are actual time and 30-day-month approximate time?
200 actual days; 198 approximate days
Actual elapsed calendar days total 200; approximate time is 30(8 − 1) + (6 − 18) = 198.
Slater_Ch16_424-447 Textbook.pdf; Slater_Ch17_448-471 Textbook.pdf; 1-1_SimpleInterest.pdf; 1-2_DiscountInterest.pdf05Under the U.S. Rule, a PHP 60,000 debt at 12% gets a PHP 15,000 payment after 3 months. What principal remains?
PHP 46,800
Interest is 60,000(.12)(.25) = 1,800. Only 13,200 of the payment reduces principal.
Slater_Ch16_424-447 Textbook.pdf; Slater_Ch17_448-471 Textbook.pdf; 1-1_SimpleInterest.pdf; 1-2_DiscountInterest.pdf06A PHP 80,000 9-month note earns 10% simple interest; it is sold 3 months before maturity at an 8% discount rate. Which amount is the discount base?
PHP 86,000 maturity value
First accumulate the original note for all nine months; the bank then discounts the amount it will collect at maturity for the three remaining months.
Slater_Ch16_424-447 Textbook.pdf; Slater_Ch17_448-471 Textbook.pdf; 1-1_SimpleInterest.pdf; 1-2_DiscountInterest.pdf07What is the correct annual-rate conversion from simple bank discount d to simple interest r for the same cash flows and term t?
r = d/(1 − dt)
Cash proceeds are F(1 − dt); cost is Fdt, so r = Fdt/[F(1 − dt)t].
Slater_Ch16_424-447 Textbook.pdf; Slater_Ch17_448-471 Textbook.pdf; 1-1_SimpleInterest.pdf; 1-2_DiscountInterest.pdf08Why must a positive-proceeds simple-discount note satisfy dt < 1?
Because P = F(1 − dt) must stay positive.
At dt = 1 all face value is withheld as discount; above 1 the algebra implies negative proceeds.
Slater_Ch16_424-447 Textbook.pdf; Slater_Ch17_448-471 Textbook.pdf; 1-1_SimpleInterest.pdf; 1-2_DiscountInterest.pdf