Question

a sum yields an interest of 2070 for the second year and an interest of 2380.50 for the third year at a certain rate of compound interest compounded annually. what is the rate of interest per annum​

Answer 1

Step-by-step explanation:

It is given that

Principal = 5000

Consider r% p.a as the rate of interest

(i) We know that

At the end of one year

Interest = Prt/100

Substituting the values

= (5000×r×1)/100

= 50r

Here

Amount = 5000 + 5r

We can write it as

5000+50r=5600

By further calculation

50r=5600−5000=600

So we get

r=600/50=12

Hence, the rate of interest is 12% p.a.

(ii) We know that

Interest for the second year = (5600×12×1)/100

= 672

So the amount at the end of second year = 5600+672

= 6272

(iii) We know that

Interest for the third year = (6272×12×1)/100

= 752.64

So the amount after third year = 6272+752.64

= 7024.64