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QUESTION: 1

In what time will Rs. 8000 amount to 40,000 at 4% per annum? (simple interest being reckoned)

Solution:

The value would increase by 4% per year. To go to 5 times it’s original value, it would require an increment of 400%. At 4% SI it would take 100 years.

QUESTION: 2

A sum of money doubles itself in 5 years. In how many years will it become four fold (if interest is compounded)?

Solution:

It would take another 5 years to double again. Thus, a total of 10 years to become four fold.

QUESTION: 3

A sum of money placed at compound interest doubles itself in 3 years. In how many years will it amount to 8 times itself?

Solution:

If it doubles in 3 years, it would become 4 times in 6 year and 8 times in 9 years.

QUESTION: 4

Divide Rs. 3903 between Amar and Akbar such that Amar’s share at the end of 7 years is equal to Akbar’s share at the end of 9 years at 4% p.a. rate of compound interest.

Solution:

Akbars’ share should be such that at 4% p.a. compound interest it should become equal to Amar’s share in 2 years. Checking thorugh the options it is clear that option (a) fits perfectly as 1875 would become 2028 in 2 years @4% p.a. compound interest.

QUESTION: 5

Sanjay borrowed Rs. 900 at 4% p.a. and Rs. 1100 at 5% p.a. for the same duration. He had to pay Rs. 364 in all as interest. What is the time period in years?

Solution:

The interest he pays per year would be 36 + 55 = 91. Thus, in 4 years the interest would amount to Rs. 364.

QUESTION: 6

If a certain sum of money becomes double at simple interest in 12 years, what would be the rate of interest per annum?

Solution:

100/12 = 8.33%

QUESTION: 7

A sum of Rs. 600 amounts to Rs. 720 in 4 years at Simple Interest. What will it amount to if the rate of interest is increased by 2%?

Solution:

600 becomes 720 in 4 years SI —> SI per year = Rs. 30 and hence the SI rate is 5%.

At 7% rate of interest the value of 600 would become 768 in 4 years. (600 + 28% of 600)

QUESTION: 8

A sum of money invested at simple interest triples itself in 8 years at simple interest. Find in how many years will it become 8 times itself at the same rate?

Solution:

In 8 years, the interest earned = 200% Thus, per year interest rate = 200/8 = 25% To become 8 times we need a 700% increase 700/25 = 28 years.

QUESTION: 9

If Rs. 1100 is obtained after lending out Rs. x at 5% per annum for 2 years and Rs. 1800 is obtained after lending out Rs. y at 10% per annum for 2 years, find x + y.

Solution:

x = Rs. 1000 (As 1000 @ 5% for 2 years = 1100).

Similarly y = Rs. 1500. x +y = 2500.

QUESTION: 10

The population of a city is 200,000. If the annual birth rate and the annual death rate are 6% and 3% respectively, then calculate the population of the city after 2 years.

Solution:

The yearly increase in the population is 3%. Thus, the population would increase by 3% each year. 200000 would become 206000 while 206000 would become 212180.

QUESTION: 11

If the simple interest is 10.5% annual and compound interest is 10% annual, find the difference between the interests after 3 years on a sum of Rs. 1000.

Solution:

At 10% compound interest the interest in 3 years would be 33.1% = Rs.331 At 10.5% simple interest the interest in 3 years would be 31.5% = Rs.315 Difference = Rs.16

QUESTION: 12

Find the compound interest on Rs. 64,000 for 1 year at the rate of 10% per annum compounded quarterly (to the nearest integer).

Solution:

64000 x (1.025)^{4} = 70644.025.

Interest 6644.025 Option (d). None of these is correct.

QUESTION: 13

Find the compound interest at the rate of 10% for 3 years on that principal which in 3 years at the rate of 10% per annum gives Rs. 300 as simple interest.

Solution:

At 10% per annum simple interest, the interest earned over 3 years would be 30% of the capital. Thus, 300 is 30% of the capital which means that the capital is 1000. In 3 years, the compound interest on the same amount would be 331.

QUESTION: 14

The population of Mangalore was 1283575 on 1 January 2001 and the growth rate of population was 10% in the last year and 5% in the years prior to it, the only exception being 1999 when because of a huge exodus there was a decline of 20% in population. What was the population on January 1, 1995?

Solution:

Solve through options to see that the value of 1200000 fits the given situation.

QUESTION: 15

Mohit Anand borrows a certain sum of money from the AMS Bank at 10% per annum at compound interest. The entire debt is discharged in full by Mohit Anand on payment of two equal amounts of Rs. 1000 each, one at the end of the first year and the other at the end of the second year. What is the approximate value of the amount borrowed by him?

Solution:

P + 2 years interest on P = 1000 + 1 years interest on 1000 + 1000 -+ 1.21P = 2100 → P = 1736 (approx).

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