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Simple and Compound Interest Problems The concept of compounding is widely used in the financial domain where the value of an investment increases exponentially over a given period of time. It’s also the underlying principle of several MBA topics such as time value of money and discounted cash flow (DCF) valuation. Being thorough in this concept will not only help you in the entrance exams but it will also help you in making wise decisions with regard to your investments. Also Check GMAT / GRE Tutorial Series Profit And Loss Simple and Compound interest Problems and SolutionsThese are some of the basic definitions and formulas to solve problems on Interest. Principal: This refers to the sum of money that is lent or borrowed. Interest: This is expressed as a percentage and it refers to the money earned on savings or extra money to be paid for the sum borrowed. Say, the interest is 20% on a loan of Rs. 100. Then the interest in the amount is Rs. 20 and at the end of the year, the amount to be paid is Rs. 120. Time: This refers to the time period for which the money is lent or the time period within which the sum of money has to be returned with interest. Also Check GMAT / GRE Tutorial Series Quadratic Equation Simple InterestAs the name suggests, the calculation of GMAT Exam simple and Compound interest Questions is quite simple. It involves multiplying the principal amount with the number of years and the rate of interest. Simple Interest Formula:
Abbreviated as SI = PTR/100 Compound InterestIn compound interest, the interest earned is reinvested in the next period of time. Or in other words, compound interest is calculated on the principal amount and the accumulated interest of the previous period. Consider an amount is compounded annually for 2 years; the principal amount with interest gained at the end of first year becomes the principal for the second year. Compound Interest Formula:
Abbreviated as Amount = P * [1 + R/100]t, when compounded annually. Sometimes, the interest is also calculated half-yearly or quarterly. When compounded semi-annually or half-yearly, Amount = P [1 + (R/2)/100]2t When compounded quarterly, Amount = P [1 + (R/4)/100]4t The present worth of Principal P due ‘ t’ years hence is given by: P/[1+ R/100]t Also Check GMAT / GRE Mathematics Tutorial Distance. Time and Speed Sample problems and solutionsLet us solve some examples to understand this concept Solution: Simple interest = 27250 – 25000 = 2250 Time = 3 years. SI = PTR / 100 → R = SI * 100 / PT R = 2250 * 100 / 25000 * 3 → R = 3%. Solution: Amount with interest after 4 years = Rs. 78000 Therefore, simple interest = 78000 – Principal. Let the principal amount be p. 78000 – p = p*4*5/100 → p=13000 Principal = 78000 – 13000 = Rs. 65000 Solution: The amount becomes 15000 in 2.5 years and 16500 in 4 years. Simple interest for (4-2.5) years = 16500 – 15000 Therefore, SI for 1.5 years = Rs. 1500. SI for 2.5 years = 1500/1.5 * 2.5 = 2500 Principal amount = 15000 – 2500 = Rs. 12500. Rate of Interest = 2500 * 100 / 12500 * 2.5 → R = 8%. Solution: Amount with CI = 3000 (1+ 5/100)2 = Rs. 3307.5 Therefore, CI = 3307.5 – 3000 = Rs. 307.5 Solution: Amount with CI = 10000 [1+ (12/2 * 100)]2 = Rs. 11236 Therefore, CI = 11236 – 10000 = Rs. 1236 Solution: Let the principal amount be x. SI = x * 2 * 8 / 100 = 4x/25 CI = x[1+ 8/100]2 – x → 104x/625 Therefore, 104x/625 – 4x/25 = 12.80 Solving which gives x, Principal = Rs. 2000. Solution: Let the rate of interest be r. 5000[1+ r/100]2 = 5000+253.125 → [1+r/100]2 = 5253.125/5000 Solving which gives [1+ r/100]2 = 1681/1600 → 1+r/100 = 41/40 → r = 2.5 Therefore, SI = 5000* 2 * 2.5/ 100 = Rs.
250. Solution: SI on Rs. 5760 for 1 year = 6912 – 5760 = Rs. 1152 Therefore, Rate of interest for 1 year = 100*1152/5760*1 = 20% Let the principal be p. Then, Principal = p[1+ 20/100]2 = 5760 Solving which gives Principal = Rs. 4000 Solution: Let the principal be Rs. x Simple interest = x*30/100 = 3x/10 T = 100*SI/PR = 100*3x/10 / x*15 = 2% This can be solved by considering the principal amount to be Rs. 100. Then, SI = Rs. 30. Then, T = 100*30/100*15 = 2% Practice problemsProblem 1 A banker lent Rs. 1000 at 3% per year and Rs. 1400 at 5% per year to a dealer. The amount must be returned to the banker when the total interest comes to Rs. 350. What is the number of years this will take?.
Answer A. Explanation (1000*t*3/100) + (1400*t*5/100) = 350 → t =3.5 Problem 2 Find the present value of Rs. 20872.5 due in 2 years at 10% rate of interest.
Answer D. Explanation: Present value = 20872.5/[1+ 10/100]2 Also read:
What will be the compound interest of rupees 4000 in 2 years when the rate of interest is 5% per annum?So, the correct answer is “410 Rs.”.
What will be the compound interest on Rupees 4000 at 6% per annum for 2 and half years then interest compounded half yearly?Detailed Solution
∴ Compound interest is Rs. 410.
What would be the compound interest obtained on an amount of Rs 4000?So, the compound interest = Rs. 5,227.20 - Rs. 4,000 = Rs. 1,227.20.
How do you calculate compound interest after 2 years?r = rate of interest. n = number of times interest is compounded per year. t = time (in years)
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Interest Compounded for Different Years.. |