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21. What is the difference between the compound interests on ₹ 5000 for 1 years at 4% per annum compounded yearly and half-yearly?
Half-yearly rate = 2%
A = 5000(1.02)^2 = 5202
CI = 5202 − 5000 = ₹ 202
Difference = 202 − 200 = ₹ 2
22. A man gets a simple interest of ₹ 1000 on a certain principal at the rate of 5 p.c.p.a. in 4 years. What compound interest will the man get on twice the principal in 2 years at the same rate?
P = 5000
Twice principal = 10000
A = 10000(1.05)^2 = 11025
CI = 11025 − 10000 = ₹ 1025
23. What will be the difference between S.I. and C.I. on a sum of ₹ 15000 for 2 years at the same rate of interest of 12½% per annum?
= 15000(0.125)^2
= ₹ 234.375
24. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of ₹ 12,000 after 3 years at the same rate?
A = 12000(1.10)^3 = 15972
CI = 15972 − 12000 = ₹ 3972
25. A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is
(CI − SI) for 3 years = P(R/100)^2 (3 + R/100)
Ratio = 25 : 8
(3 + R/100) : 1 = 25 : 8
R = 12%
26. A father left a will of ₹ 16400 for his two sons aged 17 and 18 years. They must get equal amounts when they are 20 years, at 5% compound interest. Find the present share of the younger son.
Younger grows for 3 years, elder for 2 years.
x(1.05)^3 = y(1.05)^2
⇒ x(1.05) = y ⇒ y = 1.05x
x + y = 16400
x + 1.05x = 16400
2.05x = 16400 ⇒ x = ₹ 8000
27. Mr. Dua invested money in two schemes A and B offering compound interest @ 8 p.c.p.a. and 9 p.c.p.a. respectively. If the total amount of interest accrued through two schemes together in two years was ₹ 4818.30 and the total amount invested was ₹ 27,000, what was the amount invested in Scheme A?
CI for 2 years: A = x(1.08)^2 − x = 0.1664x
B = (27000 − x)(1.09)^2 − (27000 − x) = 0.1881(27000 − x)
0.1664x + 0.1881(27000 − x) = 4818.30
Solving ⇒ x = ₹ 15000
28. A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?
⇒ (1 + R) = 2
For 16 times: 16 = 2^4
Time = 4 years
29. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is
After 4 years: (1.2)^4 = 2.0736 > 2
Hence, 4 years
30. Under the Rural Housing Scheme, the Delhi Development Authority (DDA) allotted a house to Kamal Raj for ₹ 1,26,100. This payment is to be made in three equal annual instalments. If the money is reckoned at 5% per annum compound interest, then how much is to be paid by Kamal Raj in each instalment?
Present value equation:
x/(1.05) + x/(1.05)^2 + x/(1.05)^3 = 126100
Solving ⇒ x = ₹ 46305
