Question

Interest earned on an amount at 11% rate in S.I for 4 years equal to the interest earned when same amount is invested at some interest in a scheme with C.I for 2 years.If Interest earned in C.I for 3 years is 10920 then find out the initial amount invested.​

Answer 1

Step-by-step explanation:

Solution :-

Let the invested amount be Rs. X

Rate of interest (R) = 11%

Time (T) = 4 years

We know that

Simple Interest = PTR/100

=> S.I = (X×4×11)/100

=> S.I = Rs. 44X/100 ----------(1)

Given that

Time (T) = 2 years

n = 2

We know that

Amount (A) = P[1+(R/100)]^n

=> A = X[1+(R/100)]²

=> A = X[(100+R)/100]²

We know that

Compound Interest = Amount - Principle

=> C.I. = X[(100+R)/100]² - X

=> C.I. = X[{(100+R)/100}²-1]

=> C.I. = X[(100+R)²-100²]/100²

=> C.I. = X[100²+200R+R²-100²]/100²

=> C.I. = X(200R+R²)/100² --------(2)

According to the given problem

S.I. for 4 years = C.I. for 2 years

From (1) & (2)

=> (1) = (2)

=> 44X/100 = X(200R+R²)/100²

On applying cross multiplication then

=> 44X×100² = 100X(200R+R²)

=> 440000X = 100X(200R+R²)

On cancelling 100X both sides then

=> 4400 = 200R+R²

=> R²+200R-4400 = 0

=> R²+220R-20R-4400 = 0

=> R(R+220)-20(R+220) = 0

=> (R+220)(R-20) = 0

=> R+220 = 0 (or) R-20 = 0

=> R = -220 (or) R = 20

Rate of interest can't be negative.

So, R = 20%

Now,

Given Interest earned for 3 years

= Rs. 10920

Time period = 3 years

n = 3

Now.

We know that

Amount (A) = P[1+(R/100)]^n

=> A = X[1+(20/100)]³

=> A = X[(100+20)/100]³

=> A = X(120/100)³

=> A = X(6/5)³

=> A = X(6/5)×(6/5)×(6/5)

=> A = X(6×6×6)/(5×5×5)

=> A = X(216/125

=> A = Rs. 216X/125

Now

Compound Interest = Amount - Principle

=> 10920 = (216X/125)-X

=> 10920 = (216X-125X)/125

=> 10920 = 91X/125

=> 91X/125 = 10920

=> 91X = 10920×125

=> 91X = 1365000

=> X = 1365000/91

=> X = Rs. 15000

The initial amount invested = Rs. 15000

Answer:-

The amount invested initially is Rs. 15000

Used formulae:-

→ Simple Interest = PTR/100

→ Amount (A) = P[1+(R/100)]^n

→Interest = Amount - Principle

• P = Principle
• T = Time
• R = Rate of Interest
• n = number of times the interest calculated compoundly
• S.I. = Simple Interest
• C.I. = Compound Interest

→ (a+b)² = a²+2ab+b²

Used Method:-

• Prime factorization method