Question

a sum of money at a certain rate per annum of simple interest doubles in 5 years and at a different rate triples in 12 years then find the lower rate of interest per annum​

Answer 1

Lets assume the principal is $ 1

Case 1

Maturity Amount = Principal * ( 1+r/100)^n

(1+r/100)^n = Maturity Amount/Principal

(1+r/100)^5 = 2

n=5 years

Maturity is double of principal. (2/1=2)

^ means - to the power of

(1+r/100)= 5th Root of 2 (use a calculator or excel formula 2^(1/5))

1+(r/100) = 1.1487

r/100= 1.1487–1 = 0.1487

r=14.87% (annual compunded)

Case 2

Maturity Amount = Principal * ( 1+r/100)^n

(1+r/100)^n = Maturity Amount/Principal

(1+r/100)^12 = 3

n=12 years

Maturity is triple of principal. (3/1=3)

(1+r/100)= 12th Root of 3 (use a calculator or excel forumula 12^(1/12))

1+(r/100) = 1.0959

r/100= 1.0959–1 = 0.0959

r=9.59% (annual compunded)

The lower one is 9.59%.

Answer 2

$\huge\boxed{\fcolorbox{cyan}{orange}{solution!!...}}$

$\green{\underline\textbf{at simple interest...}}$

(n - 1) x 100 = r t

$\underline\mathcal\blue{case\:1:}$

(2 - 1) x 100 = 5r

=> r = 20%

(3 - 1) x 100 = 12r

$\underline\mathcal\blue{case\:2:}$

=> r = 200/12

= 16

= 2/3%

$\green{\underline\textbf{Case 2 has lesser rate of interest...}}$

hope!!...it helps uhh...✌️❣️