Question

A sum of money becomes ` 18522 in three years and ` 19448.10 in 4 years at the same rate of interest, compounded annually. Find the sum and the rate of interest per annum.​

Answer 1

Answer:

Sum= 16,000

Interest= 5%

Formula

A= P(1+i/100m)^mn

where,

P= Original amount

A= Amount of money after ceratin years

m= number of times that the interest is compunded in 1 year(here m=1)

i= rate of interset per annum

mn= total number of times interest is compounded in n years

After 2 years,

17640=P(1+i/100*1)^2

or, 17640= P(1+0.01i)^2…………………..(i)

After 3 years,

18522=P(1+i/100*1)^3

18522=P(1+0.01i)^3…………………(ii)

Dividing (i) by (ii)

17640/18522=P(1+0.01i)^2/P(1+0.01i)^3

0.952=1/(1+0.01i)

1+0.01i=1.05

i= 5%

Now in (i)

17640=P(1+0.01*5)^2

P(1.05)^2=17640

P= 16000