# Simple and Compound Interest ( 21 to 25 )

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Questions:

21. How long will it take a sum of money invested at 5% p.a. S.I. to increase its value by 40%?

A)    5 years

B)    6 years

C)    7 years

D)    8 years

E)    None of these

Explanation:

Let the sum be x. Then, S.I. = 40% of x = 2x/5, R = 5%

Therefore, T = (100 * 2x/5 * 1/ x * 5) = 8 years.

22. How much annual payment will be discharge on a debt of Rs.4410 due in 3 years at 5% simple interest?

A)    Rs.1600

B)    Rs.1500

C)    Rs.1400

D)    Rs.1550

E)    None of these

Explanation:

Let the annual installment be Rs. X. Then,

= [x + (x * 2 * 5 / 100)] + [x + (x * 1 * 5 / 100)] + x = 4410

• 22x/20 + 21x/20 + x = 4410
• (22x + 21x + 20x) / 20 = 4410
• 63x = 4410 * 20
• x = 4410 * 20 / 63
• x = 1400

23. A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2% higher rate, it would have fetched Rs.60 more. The sum is?

A)    Rs.1000

B)    Rs.1500

C)    Rs.1600

D)    Rs.1800

E)    None of these

Explanation:

Let the sum be Rs. X and original rate be R%. Then,

• x * (R + 2) * 3 / 100 –  x * R * 3/100 = 60
• 3Rx + 6x – 3Rx = 6000
• 6x = 6000
• x = 1000

24. The time in which Rs.2000 will amount to Rs.2420 at 10% p.a. compound interest is

A)    5 years

B)    3 years

C)    4 years

D)    2 years

E)    None of these

Explanation:

Given that, P = Rs.2000, A = Rs.2420, R = 10%

Therefore, 2420 = 2000 (1 + 10/100)n

• 121/100 = (11/10)n
• (11/10)2 = (11/10)n
• n = 2 years

25. A woman borrows Rs.3825 which has to be paid back by the end of 2 years in two equal yearly installments with compound interest at the rate of 4% p.a. How much will each installment be?

A)    Rs.1275

B)    Rs.1352

C)    Rs.2028

D)    Rs.2100

E)    None of these

Explanation:

Let the value of each installment be Rs. x. Then,

(P.W. of Rs. x due 1 year hence) + (P.W. of Rs. x due 2 years hence) = Rs.3825

• x / (1 + 4/100) + x / (1 + 4/100)2 = 3825
• 25x/26 + 625x/676 = 3825
• 1275x = 3825 * 676
• x = 3825 * 676 / 1275
• x = 2028

Therefore, value of each installment = Rs.2028