What annual instalment will discharge a debt of rupees 1060 due in 4 years at 4 simple interest

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A certain sum of money amounts to rupees 2900 at 4% per annum in 4 years. In how many years will it amount to rupees 5000 at the same rate? a) 20 b) 22 c) 24 d) 25 e) None of these
Answer – d) 25
Explanation : 2900 = p + p*(4/100)*4, p = 2500 5000 = 2500 + 2500*(4/100)*t
A sum of money becomes four times at simple interest rate of 5%. At what rate it becomes seven times a) 8% b) 10% c) 12% d) 14% e) None of these
Answer – b) 10%
Explanation : 3p = p*(5/100)*t, t = 60 6p = p*(r/100)*60
Arya borrows rupees 6000 from a bank at SI. After 4 years she paid Rs 2500 to the bank and at the end of 5 years from the date of borrowing he paid Rs 4560 to settle the account. Find the rate of interest (approx) a) 3.25% b) 3.50% c) 3.85% d) 4% e) None of these
Answer – c) 3.85%
Explanation : Total interest she paid = 6000*(r/100)*4 + 3500*(r/100)*1 = 275r total interest = 2500 + 4560 – 6000 = 1060 so 1060 = 275r, r = 3.85% approx
A sum of money lent out at simple interest amounts to rupees 840 in 3 years and to rupees 1200 in 8 years. Find the rate of interest a) 11.8/13% b) 11.7/13% c) 12.8/13% d) 12.7/13% e) None of these
Answer – b) 11.7/13%
Explanation : 1200 = p + p*(r/100)*8 840 = p + p*(r/100)*3 Solve both equations to get r
The simple interest on a certain sum of money at 4% per annum for 5 years is 100 more than the interest on the same sum for 3 years at 5% per annum. Find the sum a) 1000 b) 1500 c) 2000 d) 2500 e) None of these
Answer – c) 2000
Explanation : p*(4/100)*5 – p*(5/100)*3 = 100
A sum of rupees 4800 is lent out in two parts in such a way that the interest on one part at 10% for 4 years is equal to that on another part at 8% for 7 years. Find the two sums a) 2800, 2000 b) 2400, 2400 c) 2600, 2200 d) 2700, 2100 e) None of these
Answer – a) 2800, 2000
Explanation : Let first part is A then second will be 4800 – A A*(10/100)*4 = (4800 – A)*(8/100)*7
The simple interest on a sum of money will be rupees 400 after 5 years. In the next 5 years the principal is doubled, what will be the total interest at the end of the 10th year a) 800 b) 1000 c) 1200 d) 1600 e) None of these
Answer – c) 1200
Explanation : 400 = p*(r/100)*5, pr = 8000 SI = 2p*(r/100)*5 = pr/10 = 8000/10 = 800 Total interest = 400 + 800 = 1200
What annual instalment will discharge a debt of rupees 1060 due in 4 years at 4 % simple interest? a) 200 b) 250 c) 300 d) 400 e) None of these
Answer – b) 250
Explanation : Let each instalment be P, [P + P*(4/100)*3] + [P + P*(4/100)*2] + [P + P*(4/100)*1] + P = 1060
Anil borrowed some money at the rate of 5 percent per annum for the first 2 years, 3 percent for the next 4 years and 4 percent per annum beyond 6 years. If the total interest paid by him at the end of 9 years is rupees 3400, how much money did anil borrow. a) 5000 b) 8000 c) 10000 d) 12000 e) None of these
Answer – c) 10000
Explanation : 3400 = p*(5/100)*2 + p*(3/100)*4 + p*(4/100)*3 = 3400
Saroj invested 20000 rupee in fixed deposit at the rate of 10% simple interest. After every 3 rd year he added interest to principal. Find the interest earned at the end of 6th year. a) 7800 b) 8000 c) 7600 d) 8200. e) None of these
Answer – a)7800
Explanation : For the first 3 years SI will be = 20000*10/100*3 = 6000 Now he add 6000 to the principal i.e = 20000+6000 = 26000
Now interest earned at end of 6th year = 26000*10/100*3 = 7800

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Answer

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Hint: Let Rs. x be the annual instalment. Now, x accumulates an interest of 7% every year. In this way find the value of x deposited in the 4 years and solve the question.

Complete step by step answer:

We know that,First year instalment = $x + \dfrac{{x \times {\text{interest}} \times {\text{time}}}}{{100}}$Here time = 1 year.So,$1^{st}$ year instalment = $x + \dfrac{{x \times 7 \times 1}}{{100}} = \dfrac{{107x}}{{100}}$$1^{st}$ year instalment = 1.07x.Similarly,$2^{nd}$ year instalment = $x + \dfrac{{x \times 7 \times 2}}{{100}} = \dfrac{{114x}}{{100}}$$2^{nd}$ year instalment = 1.14x.$3^{rd}$ year instalment = $x + \dfrac{{x \times 7 \times 3}}{{100}} = \dfrac{{121x}}{{100}}$$3^{rd}$ year instalment = 1.21x.$4^{th}$ year instalment = x.Now, we have to find the annual instalment that will discharge a debt of Rs.2710.So,Adding all year’s instalment,\[ \Rightarrow 1.07x + 1.14x + 1.21x + x = 2710\]\[ \Rightarrow 4.42x = 2710\]\[ \Rightarrow x = \dfrac{{2710}}{{4.42}}\]\[ \Rightarrow x = 613.12\]We can write this as: x = Rs.613.Hence, we can say that the annual instalment that will discharge a debt of Rs.2710 is Rs.613.

So, the correct answer is “Option B”.

Note: Whenever we ask such types of questions, we have to remember some basic steps. First, we have to find out all the given details. Then we will assume that x be that annual instalment. After that, we will find the amount of installments for every year and then by adding those amounts and equating it with the debt, we will get the value of x and through this, we will get the required answer.

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