8 min readConcept sheetShort calculation; 10-mark invoice or bill-discounting problem

Simple interest and discounts

Simple interest is paid only on the original principal: I = Prt. Trade discounts cut the list price; cash discounts reward early payment.

Simple interestI = P × r × t

AmountA = P(1 + rt)

Chain discountList × (1 − d₁)(1 − d₂)

Bank discountD = S × d × t; proceeds = S − D

Simple interest and discount formulas

Simple interestI = Prt (r as a decimal, t in years)

Amount (maturity value)A = P + I = P(1 + rt)

Principal from amountP = A ÷ (1 + rt)

Rater = I ÷ (Pt)

Timet = I ÷ (Pr)

Time in days (this course)t = days ÷ 365

Net price after trade discountsList price × (1 − d₁)(1 − d₂)…

Bank discount on a bill of value SD = Sdt (d = discount rate a year, t in years); proceeds = S − D

Rounding (this course)Money to 2 decimal places (cents); keep 6 or more decimal places in factors such as 1.01²⁴

Simple interest vs bank discount

Simple interestInterest is added at the end and is worked out on the amount borrowed.

Bank discountInterest is taken in advance from the maturity value, so the borrower gets less and the true rate is higher.

Simple interest

Problem

Rs. 250,000 is borrowed at 12% a year simple interest. Find (a) the interest and amount after 3 years, (b) the interest for 146 days.

Working

(a) I = Prt = 250,000 × 0.12 × 3 = 90,000.
A = P + I = 250,000 + 90,000 = 340,000.
(b) t = 146 ÷ 365 = 0.4 year.
I = 250,000 × 0.12 × 0.4 = 12,000.

Answer

(a) Interest Rs. 90,000; amount Rs. 340,000. (b) Rs. 12,000.

Finding the rate and the time

Problem

(a) Rs. 80,000 grows to Rs. 96,800 in 3 years at simple interest. Find the rate. (b) How long does Rs. 60,000 take to earn Rs. 13,500 at 9% simple interest?

Working

(a) I = 96,800 − 80,000 = 16,800.
r = I ÷ (Pt) = 16,800 ÷ (80,000 × 3) = 16,800 ÷ 240,000 = 0.07.
(b) t = I ÷ (Pr) = 13,500 ÷ (60,000 × 0.09) = 13,500 ÷ 5,400 = 2.5.

Answer

(a) 7% a year (b) 2.5 years

Trade and cash discounts

Problem

A wholesaler lists a refrigerator at Rs. 150,000 with trade discounts of 20% and 10%, and terms 2/10, n/30. Find (a) the net invoice price, (b) the amount paid if the retailer pays within 10 days, (c) the single equivalent trade discount.

Working

(a) After 20%: 150,000 × 0.8 = 120,000. After 10%: 120,000 × 0.9 = 108,000.
(b) 2/10 means 2% off if paid within 10 days: 108,000 × 0.02 = 2,160.
Amount paid = 108,000 − 2,160 = 105,840.
(c) Net factor = 0.8 × 0.9 = 0.72, so the single discount = 1 − 0.72 = 0.28.
Note: 20% and 10% is 28%, not 30%, because the second discount is taken on a smaller price.

Answer

(a) Rs. 108,000 (b) Rs. 105,840 (c) 28%

Discounting a bill at the bank

Problem

A business holds a Rs. 500,000 bill due in 90 days and discounts it at a bank at 10% a year. Find the discount, the proceeds, and the true (simple interest) rate the business pays.

Working

D = S × d × t = 500,000 × 0.10 × 90/365 = 12,328.77.
Proceeds = 500,000 − 12,328.77 = 487,671.23.
The business really borrows Rs. 487,671.23 and pays Rs. 12,328.77 for 90 days.
True rate = 12,328.77 ÷ 487,671.23 × 365/90 = 0.1025.

Answer

Discount Rs. 12,328.77; proceeds Rs. 487,671.23; true rate about 10.25%, higher than the quoted 10%.

In Sri Lankan business

Suppliers to Sri Lankan retailers give trade discounts off list prices, and invoices may offer early-payment terms such as 2/10, n/30. Real rates change, so always use the rate the question gives.

Exam angle

Short answer: “Find the simple interest on Rs. 60,000 at 9% a year for 146 days.” 60,000 × 0.09 × 146/365 = Rs. 2,160.

Short answer: “What do the terms 2/10, n/30 mean?” 2% cash discount if paid within 10 days; otherwise the full (net) amount is due within 30 days.

Essay: “Goods listed at Rs. 150,000 carry trade discounts of 20% and 10% and terms 2/10, n/30. Find the net price, the amount paid on day 8, and the single equivalent discount.” Rs. 108,000; Rs. 105,840; 28%.

Remember it

I = Prt: "Please remember time" is in years. Chain discounts multiply (0.8 × 0.9); they never simply add.