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Bharat borrowed Rs.180,000 on a condition that he had to pay 7.5% interest every year. He also agreed to pay the principal in equal annual instalments over 21 years. After a certain number of years, however, the rate of interest has been reduced to 7%. It is also known that at the end of the agreed period, he will have paid in all Rs.2,70,900 in interest. For how many years does he pay at the reduced interest rate?
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Explanation:
x = interest paid at 7.5%
(21-x) years interest paid at 7%
((180000*x*7.5)/100) + ((180000*7*(21-x))/100) = 270900
x = 7
21 – 7 = 14 years he paid at the reduced interest rate.
Ankita borrows Rs.7000 at simple Interest from a lender. At the end of 3 years, she again borrows Rs.3000 and settled that amount after paying Rs.4615 as interest after 8 years from the time she made the first borrowing. what is the rate of interest?
SI for Rs.7000 for 8 years= (7000*r*8)/100
Again borrowed=3000
SI = (3000*r*5)/100
Total interest= [(7000*r*8)/100] + [(3000*r*5)/100] = 4615
560r + 150r = 4615
710r = 4615
r = 6.5%
Hari borrowed some money for one year at 6% per annum simple interest and after 18 months , he again borrowed the same money at a Simple Interest of 24% per annum. In both the cases, he paid Rs.4704. Which of the following could be the amount that was borrowed by Hari in each case if interest is paid half yearly?
12% for 6 months
x = Borrowed money
Take x =100%
112% of x = 4704
x = 4200
Ravi lent out a part of Rs. 38800 is lent out at 6% per six months. The rest of the amount is lent out at 5% per annum after one year. The ratio of interest after 3 years from the time when first amount was lent is 5:4. Find the second part that was lent out at 5%.
First Part = x
[x * (0.06)*6] / (388800 – x)*0.05*2 = 5/4
1.44x = 19400 – 0.5x
x = 10000
Second Part = 38800 – 10000 = 28800
Harshita lent out some money at 6% Simple Interest per annum. After one year, Rs.6800 is repaid and the rest of the amount is repaid at 5% per annum. If the second year’s interest is 11/20 of the first year’s interest, find what amount of money was lent out.
P – amount lent by Harshita
I=.06*P —(i)
The interest for second year as X=(P+I-6800).05 —(ii)
x=(11/20)I —(iii)
Put (i) in (ii) and (iii)
P = 17,000
Vikram borrows a sum of Rs.1500 at the beginning of a year. After four months Rs.2100 more is borrowed at a rate of interest double the previous one. At the end of one year, the sum of interest on both the loans is Rs.416. What is the first rate of interest per annum?
P = 1500
Rate of Interest = x
SI = 1500x/100 = 15x
P = 2100
Rate of Interest = 2x
SI = 4200x/100 = 42x
57x = 416
x = 7.3%
Rahul invested a sum of money at Simple Interest at a certain rate of interest for three years. Had it been invested at a 4% higher rate, it would have fetched Rs.480 more. Find out the Principal amount that was invested by Rahul?
x – Principal
Extra amount = 4% for 3 years = 12% of x = 480
x = (480/12)*100 = 4000
Rakesh fixes the rate of interest 6% per annum for first 3 years and for the next 4 years, 7 percent per annum and for the period beyond 7 years, 7.5 percent per annum. If Mr. Rakesh lent out Rs.1500 for 11 years, find the total interest earned by him?
6% for 3 years = 18%
7% for 4 years = 28%
7.5% for 4 years = 30%
76% of 1500 = 1140
An equal amount of sum is invested in two schemes for four years each, both offering simple interest. When invested in scheme A at 8% per annum the sum amounts to Rs.5280. In scheme B, invested at 12% per annum it amounts to Rs.5920. What is the total sum invested?
Sum = x
x + [(x*4*8)/100] = 5280
33x = (5280*25) = 4000
Total sum = 2 * 4000 = 8000
Simple Interest on a certain sum at a certain annual rate of interest is 16% of the sum. If the numbers representing rate per cent and time in years be equal, then the rate of interest is?
SI = 16% of P
R = T = x
SI = [P*N*R]/100
4P/25 = [P*x^2]/100
x = 4%
Vikram invests some money in three different schemes for 4 years, 8 years and 12 years at 10%, 15% and 20% Simple Interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investments is:
Principal = x1, x2 and x3
x1 * 4 * 10 = x2 * 8 * 15 = x3 * 12 * 20
x1 = 3×2 = 6×3
x1 : x2 = 3 : 1 ; x2 : x3 = 2 : 1
x1 : x2 : x3 = 6 : 2 : 1
Mr. Ravi finds that due to a fall in the rate of interest from 9% to 6%, his yearly income diminishes by Rs.267. His capital is ?
Difference in Rate of Interest = 9% – 6% = 3%
Capital = x
3% of x = 267
x = 8900
Out of Rs. 50,000 that a man has, he lends Rs. 8,000 at 11/2 % per annum simple interest and Rs. 24,000 at 6% per annum simple interest. He lends the remaining money at a certain rate of interest so that he gets total annual interest of Rs. 3,680. The rate of interest per annum, at which the remaining money is lent, is ?
Total Amount = 50000
Amount divided into three parts – x, y, z
x = 8000, T = 1 yr
SI(x) = (8000 * 11/2)/100 = 440
y = 24000 R = 6%
SI(y) = (24000 * 6)/100 = 1440
Total Interest = 3680, Interest on the remaining amount = 3680 – 440 – 1440 = 1800
z = 50000 – 24000 – 8000 = 18000
R = (1800 * 100) /18000 = 10%
Vikram lends Rs 30,000 of two of his friends. He gives Rs 15,000 to the first at 6% p.a. simple interest. He wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is:
S.I. on Rs 15000
=(15000×6×1)/100 = Rs. 900
Profit to made on Rs 30000
= 30000×10/100=Rs 3000
S.I.on Rs.15000 = 3000-900 = Rs.2100
Rate=(S.I.* 100)/(P * T)=(2100×100)/15000
=14% per annum
Suresh lends 40% of his money at 15% per annum, 50% of the rest at 10% per annum and the rest at 18% per annum rate of interest. What would be the annual rate of interest, if the interest is calculated on the whole sum?
x – (40/100)*x = 60x/100
40/100 at 15% p.a = 40/100 * 15/100 = 60x/1000
50/100*60x/100 = 30x/100 at 10% p.a = 30x/100 * 10/100 = 30x/1000
Balance amount = x – 40x/100 – 30x/100 = 30x/100 at 18% p.a = 18/100 * 30x/100 = 54x/1000
R = [(144x/1000)/x] * 100 = 14.4%
Ajay borrows Rs 1000 at the rate of 12% per annum simple interest and Babu borrows Rs 1050 at the rate of 10% per annum simple interest. In how many years will their amounts of debts be equal?
Let Time = x years Then,
[1000+(1000*12*x)/100] = [1050+(1050*10*x)/100] => 1000 + 120x = 1050 + 105x
=> 15x = 50 ⇒ x = 10/3 years
A sum of Rs. 8800 is to be divided among three brothers Anil, Deepak and Ramesh in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 year respectively remains equal. The share of Anil is more than that of Ramesh by?
x*5*1/100 = y*5*2/100 = z*5*3/100
x:y:z = 6:3:2
The share of Anil is more than that of Ramesh by = 4/11 * 8800 = 3200
Mayank invested a certain sum of money in a simple interest bond, that value grew to Rs. 300 at the end of 3 year and to Rs. 400 at the end of another 5 year. Then what was the rate of interest in which he invested his sum?
P*R*3/100 + P = 300 –(i)
P*R*8/100 + P = 400 –(ii)
From (i) and (ii)
P*R*5/100 = 100
P*R = 2000—(iii)
Sub (iii) in (i)
6000/100 + P = 300
P = 240
240*R = 2000 => R = 8.33%
Vivek took a loan from the bank at 8% per annum, and was supposed to pay a sum of Rs.2500 at the end of 4 years. If the same sum is cleared off in four equal annual instalments at the same rate, then the amount of annual instalment will be?
x + (x*8*1/100) = 27x/25
x + (x*8*2/100) = 29x/25
x + (x*8*3/100) = 31x/25
(x + 27x/25 + 29x/25 + 31x/25) = 2500
112x/25 = 2500 => x = 558
Sachin invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest. He received yearly interest of Rs.140. But if he had interchanged the amounts invested, he would have received Rs.4 more as interest. How much did he invest at 12% simple interest?
Amount invested at 12% = Rs. x
Amount invested at 10% = Rs. y
140 = x*12*1/100 + y*10*1/100
12x + 10y = 14000 -(i)
144 = x*10*1/100 + y*12*1/100
10x + 12y = 14400 -(ii)
x = 545.45
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