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RD Sharma Solutions Class 7 Mathematics Solutions for Simple Interest Exercise 13.1 in Chapter 13 - Simple InterestQuestion 5 Simple Interest Exercise 13.1 A person deposits Rs 25000 in a firm who pays an interest at the rate of 20%per annum. Calculate the income he gets from it annually. Answer: Given Principal amount P = Rs 25000 Time period T = 1 year Rate of interest R = 20% p.a. We know that simple interest = (P × T × R)/100 On substituting these values in above equation we get SI = (25000 × 1 × 20)/100 = Rs 5000
Video transcript hello friends welcome to leader's online homework solving session today we'll be looking at the following question the questions state what are radicals and give the name of the radicals so here in this question we have to first state what is radicals and then we have to give the names of these radicals so radicals are basically it's a atom or a group of atoms of same or different elements that behave as a it may be of same or different elements that behave as a positive or negative ions these are called as radicals what does this mean is let's see an example now hydroxyl radical so so this hydroxyl radical if i want to represent it it is having one unpaired electron so here we can see there is a pairing here for a hydroxyl radical but this is unpaired electron that is we can say it is having unpaired valence electron and that is why these radicals are highly chemically reactive so that is what when i say an atom or group of atoms of same or different elements that behave as a positive or a negative ion why does they behave because of their unpaired balance electron now let's look at the names of this radicals out here so here the first one is nitrate no3 second one is hydroxide the third one so4 it is called as sulfate radical and the fourth co3 it is called as carbonate radical so friends this is how we approach this question hope you understood the solution in case if you have any doubts please feel free to drop a comment below and subscribe to this channel for regular updates thank you Was This helpful?
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. Compound 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: A = 5000(1 + 0.06/4)(4)(4) = 5000(1.015)(16) = $6344.93e) 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. Answer: 160,000What is the compound interest on a principal of 25000 after 3 years at the rate of 12% per annum?(1+12100)3=25000(2825×2825×2825)=35123.20. Q.
What will be the compound interest of 25000 for 3 years at 8% per annum compounded annually?Amount = ₹ 33264.
What is the compound interest on rupees 10000 at 10% for 3 years?10000 (1+10100)3=Rs. 10000×1110×1110×1110=Rs. 13310C.I.
What is the compound interest of 10% for 3 years?∴ The compound interest is Rs. 3,310.
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A man invested Rs 25000 at the rate of 9% for 3 years what is the compound interest
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