What is the compound interest of 8000 for 6 month at 20% per annum compounded quarterly?
Find the compound interest on Rs. 8000 for 9 months @ 12% p.a., when interest is compounded quarterly.
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Answer (Detailed Solution Below)Option 1 : 741.81 Free CT 1: Growth and Development - 1 10 Questions 10 Marks 10 Mins Given: Principal = Rs. 8000 Time = 9 Months Rate of interest = 12% p.a. Formula Used: Compound interest = Principal × (1 + Rate%/100)Time - Principal Calculation: Interest is compounded quarterly, So Time = 9/3 = 3 Rate of interest = 12%/4 = 3% p.a. Compound interest = Principal × (1 + Rate%/100)Time - Principal ⇒ Compound interest = 8000 × (1 + 3/100)3 - 8000 ⇒ Compound interest = 8741.81 - 8000 ⇒ Compound interest = Rs. 741.81 ∴ Compound interest is Rs. 741.81 The correct option is 1 i.e. Rs. 741.81 Last updated on Sep 29, 2022 REET 2022 Written Exam Result Out on 29th September 2022! The final answer key was also out with the result. The exam was conducted on 23rd and 24th July 2022. The candidates must go through the REET Result 2022 to get the direct link and detailed information on how to check the result. The candidates who will be finally selected for 3rd Grade Teachers are expected to receive Rs. 23,700 as salary. Then, the candidates will have to serve the probation period which will last for 2 years. Also, note during probation, the teachers will receive only the basic salary. Ace your Interest preparations for Compound Interest with us and master Quantitative Aptitude for your exams. Learn today! Simple Interest: A = P(1+rt)P: the principal, the amount invested A: the new balance t: the time r:the rate, (in decimal form)Ex1: If $1000 is invested now with simple interest of 8% per year. Find the new amount after two years. P = $1000, t = 2 years, r = 0.08. A = 1000(1+0.08(2)) = 1000(1.16) = 1160Compound Interest:P:the principal, amount invested A: the new balance t: the time r:the rate, (in decimal form) n: the number of times it is compounded. Ex2:Suppose that $5000 is deposited in a saving account at the rate of 6% per year. Find the total amount on deposit at the end of 4 years if the interest is: P =$5000, r = 6% , t = 4 yearsa) simple : A = P(1+rt) A = 5000(1+(0.06)(4)) = 5000(1.24) = $6200b) compounded annually, n = 1: c) compounded semiannually, n =2: A = 5000(1 + 0.06/2)(2)(4) = 5000(1.03)(8) = $6333.85d) compounded quarterly, n = 4: e) compounded monthly, n =12: A = 5000(1 + 0.06/12)(12)(4) = 5000(1.005)(48) = $6352.44f) compounded daily, n =365: A = 5000(1 + 0.06/365)(365)(4) = 5000(1.00016)(1460) = $6356.12Continuous Compound Interest:Continuous compounding means compound every instant, consider investment of 1$ for 1 year at 100% interest rate. If the interest rate is compounded n times per year, the compounded amount as we saw before is given by: A = P(1+ r/n)ntthe following table shows the compound interest that results as the number of compounding periods increases: P = $1; r = 100% = 1; t = 1 year
As the table shows, as n increases in size, the limiting value of A is the special number e = 2.71828If the interest is compounded continuously for t years at a rate of r per year, then the compounded amount is given by: A = P. e rtEx3: Suppose that $5000 is deposited in a saving account at the rate of 6% per year. Find the total amount on deposit at the end of 4 years if the interest is compounded continuously. (compare the result with example 2) P =$5000, r = 6% , t = 4 years A = 5000.e(0.06)(4) = 5000.(1.27125) = $6356.24Ex4: If $8000 is invested for 6 years at a rate 8% compounded continuously, find the new amount: P = $8000, r = 0.08, t = 6 years. A = 8000.e(0.08)(6) = 8000.(1.6160740) = $12,928.60Equivalent Value:When a bank offers you an annual interest rate of 6% compounded continuously, they are really paying you more than 6%. Because of compounding, the 6% is in fact a yield of 6.18% for the year. To see this, consider investing $1 at 6% per year compounded continuously for 1 year. The total return is: A = Pert = 1.e(0.06)(1) = $1.0618 If we subtract from $1.618 the $1 we invested, the return is $0.618, which is 6.18% of the amount invested. The 6% annual interest rate of this example is called the nominal rateThe 6.18% is called the effective rate.
Ex6: An amount is invested at 7.5% per year compounded continuously, what is the effective annual rate? the effective rate = er - 1 = e 0.075 - 1 = 1.0079 - 1 = 0.0779 = 7.79%Ex7: A bank offers an effective rate of 5.41%, what is the nominal rate? er - 1 = 0.0541 er = 1.0541 r = ln 1.0541 then r = 0.0527 or 5.27%Present Value:If the interest rate is compounded n times per year at an annual rate r, the present value of a A dollars payable t years from now is: If the interest rate is compounded continuously at an annual rate r, the present value of a A dollars payable t years from now is P = A. e-rtEx8: how much should you invest now at annual rate of 8% so that your balance 20 years from now will be $10,000 if the interest is compounded a) quarterly: P = 10,000.(1+0.08/4)-(4)(20)= $ 2,051.10 b) continuously: P = 10,000.e-(0.08)(20) = $2.018.974.3: The Growth, Decline Model:Same formulas will be applied for population, cost ...:Growth: P(t) = Po . ektDecline: P(t) = Po . e-kt
For compounded continuously, the time T it takes to double the price, population or balance using k as the rate of change, the growth rate or the interest rate is given by: ===>Note: the time it takes to triple it is T = ln3/k and so on..., (only if it is compounded continuously).Ex9: The growth rate in a certain country is 15% per year. Assuming exponential growth : a) find the solution of the equation in term of Po and k. b) If the population is 100,000 now, find the new population in 5 years. c) When will the 100,000 double itself? Answer: a) Po. e 0.15t; b) 211,700; c) 4.62 yearsEx10: If an amount of money was doubled in 10 years, find the interest rate of the bank. Answer: 6.93%Ex11: In 1965 the price of a math book was $16. In 1980 it was $40. Assuming the exponential model : a) Find k (the average rate) and write the equation. b) Find the cost of the book in 1985. c) After when will the cost of the book be $32 ? Answer: a) 6.1%; b) $ 54.19; c) T = 11.36 yearsEx12: How long does it take money to triple in value at 6.36% compounded daily? Answer: 17.27 yearsEx13: A couple want an initial balance to grow to $ 211,700 in 5 years. The interest rate is compounded continuously at 15%. What should be the initial balance? Answer: $100,000Ex14: The population of a city was 250,000 in 1970 and 200,000 in 1980 (Decline). Assuming the population is decreasing according to exponential-decay, find the population in 1990. What is the compound interest on 8000 at 20% per annum for 9 months compounded quarterly?So, the compound interest on Rs 8000 at 20% per annum for 9 months compounded quarterly is 1261.
What will be the compound interest on Rupees 8000 at 16% per annum for 6 months when interest is compounded quarterly?By putting the given values in above equation, =8000(1+20. 16)2×1=8000(1. 08)2=9331.
How do you calculate compound interest compounded quarterly?Cq = P [ (1+r)4*n – 1 ]. Cq is the quarterly compounded interest.. P would be the principal amount.. r is the quarterly compounded rate of interest.. n is the number of periods.. At what rate percent per annum compound interest will 8000 amount to 8820 in 6 months the interest being compounded quarterly?∴ Rate of Interest is 5% per annum.
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