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QUESTION: 1

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:

Solution:

QUESTION: 2

What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?

Solution:

Amount after 3 years = P(1 + R/100)^{T}

=> 40000(1 + 11/100)^{3}

=> 40000(111/100)^{3}

=> 40000[(111*111*111)/(100*100*100)]

=> (4*111*111*111)/100

=> 54705.24

Compound Interest = 54705.24 - 40000

= Rs. 14705.24

QUESTION: 3

**Q.** What is the difference between the compound interests on Rs. 5000 for 1^{1/2 } years at 4 percent per annum compounded yearly and half yearly?

Solution:

QUESTION: 4

If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 60, what is the compound interest on the same at the same rate and for the same time?

Solution:

QUESTION: 5

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?

Solution:

[15000×(1+R/100)^{2} − 15000] - (15000×R×2)/100 = 96

⇒15000[(1+R/100)^{2} − 1 − 2R/100]=96

⇒ 15000[(100+R)^{2} − 10000−(200×R)]/10000 = 96

⇒ R2 = (96×23) = 64

⇒ R = 8

∴ Rate = 8%

QUESTION: 6

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:

Solution:

Amount = Rs.(30000+4347) = Rs.34347

let the time be n years

Then,30000(1+7/100)^{n} = 34347

(107/100)^{n} = 34347/30000

= 11449/10000

= (107/100)^{2}

n = 2years

QUESTION: 7

At what rate of compound interest per annum will a sum of Rs. 1400 become Rs. 1573.04 in 2 years?

Solution:

Let the rate be R% per annum

P(1+R/100)T = 1573.04

= 1400(1+R/100)2 = 1573.04

= (1+R/100)2 = 1573.04/1400 = 157304/140000 = 11236/10000

(1+R/100) = (√11236/10000)

= (√11236)/(√10000)

= 106/100

R/100 = (106/100 − 1)

=> 6/100

R = 6%

QUESTION: 8

There is 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 14,000 after 3 years at the same rate?

Solution:

Simple interest = P * r * t /100, where, P is the Principal, r is the rate of interest and t is the time period such that the rate of interest and the time period have mutually compatible units like r % per annum and t years.

Here, in the first case, let the Principal be Rs.P and rate of interest be r % per annum. Time period is given as 8 years . Interest is given as 80 P / 100

So, 80 P / 100 = P * r * 8 / 100

Or, 80 = 8 r

So, r = 10 % per annum.

Now, in the second case, Principal is given as Rs. 14,000, rate of compound interest is 10 % per annum as determined above; and t is 3 years.

Compound interest = P * ( 1 + r/100)t - P

= 14,000 * ( 1+ 10 /100)3 - 14,000

= 14,000 * ( 1 + 0.1)3 - 14,000

= 14,000 *(1.1)3 - 14,000

(14,000 * 1.331) - 14,000

= 18,634 - 14,000 = 4,634

So, the compound interest on Rs.14,000 at the same rate of interest as in case 1 in 3 years will be Rs. 4,634.

QUESTION: 9

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum is:

Solution:

QUESTION: 10

The difference between simple interest and compound on Rs. 900 for one year at 10% per annum reckoned half-yearly is:

Solution:

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