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2 Commission paid is = ×750 000 100 = sh. 15 000 Interest Simple interest If you borrow money from a bank or other financial institution then you will have to pay interest (the charge paid for borrowing) in addition to your repayments. The money borrowed or lent is called the principal. When interest is paid at fixed intervals, yearly, half-yearly, quarterly or monthly, the principal is said to be lent (or borrowed) at simple interest. The interest is calculated on the original principal only. The investor receives interest at regular periods, the principal remains the same. Simple interest is calculated using the following formula P×R× T Interest = 100 Where, P = principal, R = rate of interest per annum (%); T = time (in years). Note that the units for R and T must be consistent, i.e. If R is per annum, T must be in years, If R is per month, T must be in months, e.t.c. When the simple interest for any given time is added to the principal, the sum is called the amount at simple interest for that time. Amount = Principal + Interest, i.e. A = P + I. Example Find the simple interest on sh. 25 000 for 3.5 years at 18% per annum. Solution I = P×R× T 100 Example 25000 ×18 ×3.5 = 100 = sh. 15 750. 3 1 Find the simple interest on sh. 20 000 for 1 years at 1 % per month. Find 4 2 3 also, the amount after 1 years. 4 Solution 3 1 Time = 1 years × 12 = 21 months; P = sh. 20 000; R = 1 % per month 4 2
1 20000 ×1 2 × 21 Therefore, = sh. 6 300. 100 Amount = Principal + Interest = 20 000 + 6 300 = sh. 26 300. Compound interest In most financial institutions, interest is added to the money borrowed or lent and then the interest is calculated on this total amount for the next period. Adding the interest is known as compounding the interest, or just compound interest. Compound interest = Final amount – original principal. Note: Simple interest is the same for each period, compound interest becomes greater for successive periods. Example Calculate the compound interest on sh. 2 000 for 2 years at 8% per annum. Solution First year: Principal = 2 000 Interest = 160 calculated as I = Amount = 2000 + 160 = 2 160 Second year: Principal = 2 160 2000 ×8×1 = 160 100 2160 ×8×1 Interest = 172.80, calculated as I 2 = = 172.80 100 Amount = 2 160 + 172.80 = 2 332.80 Compound interest = Amount – Principal = 2 332.80 – 2 000 = sh. 332.80 Alternatively, the compound interest can be calculated using the following formula: A = P 1 + R n 100 where, A is the amount after n years; P = principal; R is the rate % p.a. and n is the number of years. If interest is added half yearly, the value of R is half of the given R% p.a. value and n is doubled. So, when P = 2 000, R = 8 and n = 2, Amount = 2000(1.08) 2 = 2 332.80 Interest = Amount – principal = 2 332.80 – 2000 = sh. 332.80
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Page 3 and 4: Significant figures (sf) Significan
Page 5 and 6: Exercise 1. A man in Nairobi receiv
Page 7: 3. A radio that cost sh. 15 000 was
Page 11 and 12: 8. A business man had sh. 1 200 000
Page 13 and 14: 2. A dealer marks a price sh. 4 800
Page 15 and 16: (ii) income tax (sh.) 10 100 000 10
Page 17 and 18: (b) Express the total income tax fo
Page 19 and 20: O is at the vertex of the angle, an
Page 21 and 22: Exercise 1. In the figure shown, x
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Page 27 and 28: 5. The floor of a school hall is re
Page 29 and 30: (i) Compass bearings On a compass,
Page 31 and 32: N A B 15km S 75 0 A Then we choose
Page 33 and 34: - We measure AB = 4.8cm. But 1cm re
Page 35 and 36: Types of polygons Name Number of si
Page 37 and 38: 50 0 +w +x = 180 0 50 0 + 50 0 + x
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