Table of contents 
What are Interest Rates? 
Types of Interest Rates 
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Interests are of two types:
RESULTS  APPLICATION  SOLUTION 
If rate to interest is r_{1}% for T_{1} years, r_{2}% for T_{2} years …. r_{n} for T_{n} years for an investment. And if the Simple Interest obtained is ₹a on the investment. Then the principal amount is given by a x 100/ (r_{1}T_{1} + r_{2}T_{2} + …+ r_{n}T_{n})  Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond 5 years. If he pays a total interest of ₹ 11400 at the end of nine years, how much money did he borrow?  In this case, r_{1} = 6%, T_{1} = 2 years r_{2} = 9%, T_{2} = 3 years r_{3} = 14%, T_{3} = 4 years (since, beyond 5 years rate is 14%) and Simple interest = ₹11400 Therefore, P = (11400 x 100)/ (6*2 +9*3 +14*4) = 1140000/ (12 + 27 + 56) = 1140000/ 95 = ₹12000 
If a person deposits sum of ₹A at r_{1}% p.a. and sum of ₹B at r_{2}% p.a. then the rate of interest for whole sum is R = {(Ar_{1 }+ Br_{2})/ (A + B)}  A man invested 1/3 of his capital at 7%; ¼ at 8% and the remainder at 10%. If his annual income is ₹561, What is his capital?  Let x be his capital or principal. Therefore, R = (^{1}/_{3} x * 0.07 +¼ x *0.08 +^{5}/_{12} x*0.10)/x R = (^{1}/_{3} * 0.07 +¼ *0.08 +^{5}/_{12} *0.10) R = 0.08496 Total SI = ₹561 ₹561 = 0.08496x x = ₹6602 
If a sum of money becomes “n” times in “T years” at Simple Interest, then the rate of interest p.a. is R = 100(n – 1) / T  The rate at which a sum becomes 4 times of itself in 15 years at S.I. will be?  It’s a very easy question you just need to use this formula and you will directly reach to an answer. Therefore, R = (100 x 3)/15 = 20% 
If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained at simple interest on each part where interest rates are R1, R2, … , Rn respectively and time periods are T1, T2, … , Tn respectively, then the ratio in which the sum will be divided in n parts can be given by 1/R_{1}T_{1:} 1/R_{2}T_{2}:..:1/R_{n}T_{n}
 A person invests money in three different schemes for 6 years, 10 years and 12 years at 10%, 12% and 15% Simple Interest respectively. At the completion of each scheme, he gets the same interest. What is the ratio of his investment?  Here, T_{1 }= 6, T_{2} = 10 and T_{3} = 12 years resp. And, R_{1} = 10%, R_{2} = 12%, and R_{3} = 15% resp. Hence, the ratio of his investment will be 100/60 : 100/120 : 100/180 1/6 : 1/12 : 1/18 1 : 1/2 : 1/3 6 : 3 : 2 
Question 1: A man invests ₹ 5000 for 3 years at 5% p.a. compounded interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year.
 Here, P = ₹5000, T = 3 years, r = 5%. Therefore, Interest at the end of 1^{st} year = 5000 (1 + 0.05) – 5000 = ₹250
 Now Income tax is 20% on the interest income so the leftover interest income after deducing income tax = (1 – 0.2) * 250 = ₹200
Total Amount at the end of 1^{st} year = ₹5000 + 200 = ₹5200 Interest at the end of 2^{nd} year = 5200 (1 + 0.05) – 5200 = ₹260
Interest income after Income tax = 0.8 * ₹260 = ₹208
Total Amount at the end of 2^{nd} year = ₹5200 + 208 = ₹5408 Interest at the end of 3^{rd} year = ₹5408 (1.05) – 5408 = ₹270.4
Interest income after Income tax = 0.8 * ₹270.4 = ₹216.32
Total Amount at the end of 2^{rd} year = ₹5408 + 216.32 = ₹5624.32
Question 2: A sum of ₹12000 deposited at compound interest becomes double after 5 years. After 20 years, it will become?
 Principal, P = Rs. 12000;
Rate of interest = r%;
Number of years, n = 5;
Amount, A = Rs (2 × 12000) = Rs. 24000
According to the question,
24000 = 12000 × (1 + r/100)5
⇒ (1 + r/100)5 = 2 ...(i) For next part,
Principal, P = Rs. 12000;
Rate of interest = r%;
Number of years, n = 20;
Amount = Rs. x
According to the question,
x = 12000 × (1 + r/100)^{20}
⇒ x = 12000 × (1 + r/100)^{5 × 4}
⇒ x = 12000 × [(1 + r/100)^{5}]^{4}
⇒ x = 12000 × 2^{4} ...[from (i)]
⇒ x = 192000
∴ After 20 years it will become Rs. 1,92,000Shortcut Trick
12000 becomes twice in 5 years = 12000 × 2 = 24000
After another 5 years = 24000 × 2 = 48000
After another 5 years = 48000 × 2 = 96000
After another 5 years = 48000 × = 1,92,000
∴ After 20 years sum will be = 192000
Let a person takes a loan from bank at r% and agrees to pay loan in equal installments for n years. Then, the value of each installment is given by
P = X/ (1 + r/100)^{n}………X/ (1 + r/100)^{2} + X/ (1 + r/100)
Example: One can purchase a flat from a house building society for ₹ 55000 or on the terms that he should pay ₹ 4275 as cash down payment and the rest in three equal installments. The society charges interest at the rate 16% p.a. compounded halfyearly. If the flat is purchased under an installment plan, find the value of each installment.
 The cost of the flat is ₹ 55000. Now, if the person could either buy flat by paying ₹55000 or through installment plan. Since the flat was purchased through installment plan then the loan amount = ₹55000 – 4275 (down payment) = ₹50725.
 Here r = 16% compounded Halfyearly in 3 equal instalments. Let x be the amount of installment.
 Then, ₹50725 = x/ (1 + 16/200)^{3} + x/ (1 + 16/200)^{2} + x/ (1 + 16/200)
₹50725 = x (1/1.2591 + 1/1.1664 + 1/1.08)
₹50725 = x (0.79421 + 0.85722 + 0.9259)
₹50725 = x (2.577)
₹50725/2.5777 = x x = ₹19683
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