Question

Determine the rate of interest at which a sum of money will become 216 /125 times the original amount in 3/ 2 years, if the interest is compounded half yearly

Answer 1

Let the principal amount be ₹ P and the rate of interest be R% per annum.

For the interest compounded half yearly:


Time = 3/2 years = 2×3/2= 3years

Rate of interest (R%) = R/2

Given: amount at the end of 3 years must become to 216P/125

A= 216P/125

A= P(1+R/00)^n

216P/125= P ( 1+ R/200)³

216/125 = ( 1+ R/200)³

(6/5)³ = ( 1+ R/200)³

(6/5) = ( 1+ R/200)

6/5-1 = R/200

(6-5)/5 = R/200

1/5 = R/200

R= 200/5 = 40%

Hence, the rate of interest (R)= 40%

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Hope this will help you...

Answer 2

Answer:

40% p.a

Step-by-step explanation:

Let the principal amount be ₹ P and the rate of interest be R% per annum.

For the interest compounded half yearly:

Time = 3/2 years = 2×3/2= 3years

Rate of interest (R%) = R/2

Given: amount at the end of 3 years must become to 216P/125

A= 216P/125

A= P(1+R/00)^n

216P/125= P ( 1+ R/200)³

216/125 = ( 1+ R/200)³

(6/5)³ = ( 1+ R/200)³

(6/5) = ( 1+ R/200)

6/5-1 = R/200

(6-5)/5 = R/200

1/5 = R/200

R= 200/5 = 40%

Hence, the rate of interest (R)= 40%

Hope this will help you