ContactNo. :9555202436,97167611362ABHINAY MATHS CLASSESQ 1.Find the C.I. of Rs. 7500 at 4% per annum for2 years.Q 2.Find the C.I of Rs. 7500 at 4% for 1 year. If theinterest compounded half yearly.Q 3.What will be the C.I. of Rs. 10,000 at 5% per annumfor 3 years.Q 4.Find the rate of interest, if the S.I. for 3 years isRs. 1200 and C.I. for 2 years is Rs. 860.Q 5.Find the rate of interest, if S.I. for 5 years is Rs. 4000and C.I. for 2 years is 1632.Q 6.Rs. 2500 was borrowed for 3 years. What will be thecompound interest if the rate of interest for first yearis 3% per annum, second year is 4% per annum andfor third year is 5% per annum respectively?Q 7.S.I. on a sum of money is Rs. 750 for 2 years at 10%per annum. Find the C.I. on that sum for 2 years.Q 8.Find the Principal amount. If the difference of. S.Iand C.I at 12.5% per annum for 3 years is Rs. 750.Q 9.Find that principal amount on which the differenceof interest for 9 months yearly and quarterly isRs. 18.30 at 20%per annum.Q 10.A sum of money amounts to Rs. 650 in 1 year andRs. 676 in 2 years. Find that sum and rate of interest.Q 11.A sum of money amounts to Rs. 2400 in 3 years andRs. 2520 in 4 years on C.I. Find the rate of interest.Q 12.A sum of money amounts to Rs. 4500 in 2 years andRs. 6750 in 4 years Compound Interest. Find the sum.Q 13.A sum of money amounts to Rs. 3200 in 4 years andRs. 8000 in 8 years on compound interest. Find thesum.Q 14.A sum of money doubles itself at compound interestin 4 years. In how many years will it become 8 times?Q 15.A sum of money becomes 3 times of itself in 6 yearsat compound interest. In how many years will itbecome 81 times?Q 16.A sum of money becomes 4 times of itself in 6 yearsat C.I. In how many years will it become 8 times.Q 17.A sum of money becomes 8 times of itself in 12years at C.I. In how many years it will become 16times of itself.Q 18.A sum of money doubles itself in 10 years. How muchtime it will take to become 8 times if compoundedhalf yearly?Q 19.A sum of money becomes 16 times of itself in 2 yearsif compounded half yearly. How much time it willtake to become 27 times if compounded yearly.COMPOUND INTEREST Show Commercial Arithmetic II Mathematics Form 3 Notes and K.C.S.E Topical Q&A Commercial Arithmetic II – Mathematics Form 3 Notes and K.C.S.E Topical Q&ASimple Interest
Simple Interest FormulaeSimple interest = principle x rate x time Franny invests ksh 16,000 in a savings account. She earns a simple interest rate of 14%, paid annually on her investment. She intends to hold the investment for 1½years. Determine the future value of the investment at maturity. Solution I = PRT Example Calculate the rate of interest if sh 4500 earns sh 500 after 1½years. Solution From the simple
interest formulae Commercial Arithmetic II – Mathematics Form 3 Notes and K.C.S.E Topical Q&AExample Esha invested a certain amount of money in a bank which paid 1 2% p.a. simple interest. After 5 years, his total savings were sh 5600.Determine the amount of money he invested initially. Solution Let the amount invested be sh P Compound Interest
Example Moyo lent ksh.2000 at interest of 5% per annum for 2 years. First we know that simple interest for 1 st year and 2nd year will be same i.e. = 2000 x 5 x 1/100 = Ksh. 100 Total simple interest for 2 years will be = 100 + 100 = ksh. 200 In Compound Interest (CI) the first year Interest will be same as of Simple Interest (SI) i.e. Ksh.100. But year II interest is calculated on P + SI of 1 st year i.e. on ksh. 2000 + ksh. 100 = ksh. 2100. So it is Ksh. 5 more than the simple interest. This increase is due to the fact that SI is added to the principal and this ksh. 105 is also added in the principal if we have to find the compound interest after 3 years. Direct formula in case of compound interest is Types of Question
Commercial Arithmetic II – Mathematics Form 3 Notes and K.C.S.E Topical Q&AType 1Example Find the amount of ksh. 1000 in 2 years at 10% per annum compound interest. Solution. A = P (1 + r/100)t Example Find the amount of ksh. 6250 in 2 years at 4% per annum compound interest. Solution A = P (1 + r/100)t = 6250 (1 + 4/100)2 Example What will be the compound interest on ksh 31 250 at a rate of 4% per annum for 2 years? Solution. CI = P (1 + r/100)t − 1 Example A sum amounts to ksh. 24200 in 2 years at 10% per annum compound interest. Find the sum ? Solution. A = P (1 + r/100)t Type IIExample. The time in which ksh. 15625 will amount to ksh. 17576 at 4% compound interest is? Solution A = P (1 + r/100)t Example The rate percent if compound interest of ksh. 15625 for 3 years is Ksh. 1951. Solution. A = P + CI Commercial Arithmetic II – Mathematics Form 3 Notes and K.C.S.E Topical Q&AType IV
Example Find the compound interest on ksh.5000 at 20% per annum for 1.5 year compound half yearly. Solution. When interest is compounded half yearly Example Find compound interest ksh. 47145 at 12% per annum for 6 months, compounded quarterly. Solution. As interest is compounded quarterly Example Find the compound interest on ksh. 1 8750 for 2 years when the rate of interest for 1st year is 4% and for 2nd year 8%. Solution. A = P (1 + R1/100) (1 + R1/100) Commercial Arithmetic II – Mathematics Form 3 Notes and K.C.S.E Topical Q&AType VExample The compound interest on a certain sum for two years is ksh. 52 and simple interest for the same period at same rate is ksh. 50, find the sum and the rate. Solution. We will do this question by basic concept. Simple interest is same every year and there is no difference between SI and CI for 1 st year. The difference arises in the 2nd year because interest of 1 st year is added in principal and interest is now charged on principal + simple interest of 1 st year. So
in this question Now CI for 1 st year = 52 – 25 = Ksh. 27 This additional interest 27 -25 = ksh. 2 is due to the fact that 1 st year SI i.e. ksh. 25 is added in principal. It means that additional ksh. 2 interest is charged on ksh. 25. Rate % = 2/25 x 100 = 8% Shortcut: Rate % = [(CI – SI)/(SI/2)] x 1 00 Example A sum of money lent CI amounts in 2 year to ksh. 8820 and in 3 years to ksh. 9261 . Find the sum and rate. Solution. Amount after 3 years = ksh. 9261 Commercial Arithmetic II – Mathematics Form 3 Notes and K.C.S.E Topical Q&AAppreciation and DepreciationAppreciation is the gain of value of an asset while depreciation is the loss of value of an asset. Example An iron box cost ksh 500 and every year it depreciates by 1 0% of its value at the beginning of that that year. What will its value be after value 4 years? Solution Value after the first year = sh (500 − 10 x
500) In general if P is the initial value of an asset, A the value after depreciation for n periods and r the rate of depreciation per period. Example A minibus cost sh 400000.Due to wear and tear, it depreciates in value by 2 % every month. Find its value after one year, Solution A=P(1 − r/100)n Example The initial cost of a ranch is sh.5000, 000.At the end of each year, the land value increases by 2%.What will be the value of the ranch at the end of 3 years? Solution The value of the ranch after 3 years =sh 5,000, 000(1 + 2/100)3 Commercial Arithmetic II – Mathematics Form 3 Notes and K.C.S.E Topical Q&AHire Purchase
Example Achieng wants to buy a sewing machine on hire purchase. It has a cash price of ksh 7500. She can pay a cash price or make a down payment of sh 2250 and 15 monthly instalments of sh.550 each. How much interest does she pay under the instalment plan? Solution Total amount of instalments = sh 550 x 15 = sh 8250 Note;
Income Tax
Relief
Example Mr. John earns a total of K£ 12300 p.a.Calculate how much tax he should pay per annum.Using the tax table below.
Solution His salary lies between £ 1 and £1 2300.The highest tax band is therefore the third band. For the first £5808, tax due is sh 5808 x 2 = sh 11616 Commercial Arithmetic II – Mathematics Form 3 Notes and K.C.S.E Topical Q&AExample Mr. Ogembo earns a basic salary of sh 15000 per month.in addition he gets a medical allowance of sh 2400 and a house allowance of sh 12000.Use the tax table above to calculate the tax he pays per year. Solution Taxable income per month = sh (15000 + 2400 + 12000) = sh.29400 Tax due PAYE
Commercial Arithmetic II – Mathematics Form 3 Notes and K.C.S.E Topical Q&AHousing
Example Mr. Omondi who is a civil servant lives in government house who pays a rent of sh 500 per month. If his salary is £9000 p.a, calculate how much PAYE he remits monthly. Solution Basic salary £ 9000 Housing £ 15 x 9000 = £1350 Taxable income Tax charged; PAYE = sh 11670 Example Mr. Odhiambo is a senior teacher on a monthly basic salary of Ksh. 1 6000.On top of his salary he gets a house allowance of sh 1 2000, a medical allowance of Ksh.3060 and a hardship allowance of Ksh 3060 and a hardship allowance of Ksh.4635.He has a life insurance policy for which he pays Ksh.800 per month and claims insurance relief.
Solution
Past KCSE Questions on the Topic.
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