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# Compound Interest

1.

What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?

C.I. when interest is compounded yearly

= [5000 * (1 + 4/100) * (1 + (1/2 * 4)/100]

= 5000 * 26/25 * 51/50 = Rs. 5304

C.I. when interest is compounded half-yearly

= [5000 * (1 + 2/100)⊃2;]

= (5000 * 51/50 * 51/50 * 51/50) = Rs. 5306.04 Difference = (5306.04 - 5304) = Rs. 2.04

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2.

The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?

Let the rate of interest be R% p.a.

4400{[1 + R/100]⊃2; - 1} = 11193.60

[1 + R/100]⊃2; = (44000 + 11193.60)/44000

[1 + R/100]⊃2; = 1 + 2544/1000 = 1 + 159/625

[1 + R/100]⊃2; = 784/625 = (28/25)2

1 + R/100 = 28/25

R/100 = 3/25

Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100

=Rs.10560

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3.

The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?

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4.

Ramesh gets double the amount in 9 years when invested at compound interest. In how many years will the amount become four times itself?

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5.

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

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6.

Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?

64000* 9/8 * 9/8 = 81000

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7.

At the end of 2 years difference between simple and compound interest is Rs. 2166. If the principal is Rs. 60000, then what is the rate of interest?

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8.

A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself?

100 ---- 200 ---- 4

400 ---- 4

800 ---- 4

------

12 years

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9.

A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.

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10.

Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?

Let x be the investment of Ravi in 6% and y be in 7%

x(6)(n)/100 = y(7)(n)/100

=> x/y = 7/6

x : y = 7 : 6

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