What is the rate of interest p.c.p.a.?

I. An amount doubles itself in 5 years on simple interest.

II. Difference between the compound interest and the simple interest earned on a certain amount in 2 years is Rs. 400.

III. Simple interest earned per annum is Rs. 2000

Rs.100 invested in compound interest becomes Rs.200 in 5 years.

The amount will double again in another 5 years.

i.e., the amount will become Rs.400 in another 5 years.

So, to earn another Rs.200 interest, it will take another 5 years.

Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.

The extra interest earned on the compound interest bond = Rs.55

The interest for the first year =550/2 = Rs.275

Therefore, the rate of interest =55275*100= 20% p.a.

20% interest means that Shawn received 20% of the amount he invested in the bonds as interest.

If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the  bonds =27520*100 = 1375. 

As he invested equal sums in both the bonds, his total savings before investing = 2 x 1375 =Rs.2750.

Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11

Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400

Therefore Shyam's share = (441/841) * 5887 = 3087

when interest is reckoned using compound interest, interest being compounded annually. The difference in the simple interest and compound interest for two years is on account of the interest paid on the first year's interest  Hence 12% of simple interest = 90 => simple interest =90/0.12 =750.

As the simple interest for a year = 750 @ 12% p.a., the principal =750/0.12 = Rs.6250.

If the principal is 6250, then the amount outstanding at the end of 3 years = 6250 + 3(simple interest on 6250) + 3 (interest on simple interest) + 1 (interest on interest on interest) = 6250 +3(750) + 3(90) + 1(10.80) = 8780.80.

5% is the rate of interest. 20% of the interest amount is paid as tax.

i.e  80% of the interest amount stays back.

 if we compute the rate of interest as 80% of 5% = 4% p.a., we will get the same value.

The interest accrued for 3 years in compound interest = 3 x simple interest on principal + 3 x interest on simple interest + 1 x interest on interest on interest.

= 3 x (200) + 3 x (8) + 1 x 0.32 =600 + 24 + 0.32 = 624.32

The amount at the end of 3 years = 5000 + 624.32 = 5624.32

The population grew from 3600 to 4800 in 3 years. That is a growth of 1200 on 3600 during three year span.

Therefore, the rate of growth for three years has been constant.

The rate of growth during the next three years will also be the same.

Therefore, the population will grow from 4800 by 4800*13= 1600

Hence, the population three years from now will be 4800 + 1600 = 6400

The usual way to find the compound interest is given by the formula A = .p(1+r/100)^n

In this formula,

A is the amount at the end of the period of investment

P is the principal that is invested

r is the rate of interest in % p.a

And n is the number of years for which the principal has been invested.

In this case, it would turn out to be A =1500(1+20/100)^3

= 2592.

Let the sum be Rs. P.

Then,[p(1+10/100)2-p]=525

Sum =Rs.2500

S.I.= Rs.(2500*5*4)/100

= Rs. 500