Question

Find the sum on which the compound interest for 3 years at 10 % per

annum amounts to ` 1,655​

Answer 1

Answer:

• Principal sum = 1243.43

Explanation:

Given

• Time for interest, t = 3 yrs
• Rate of interest, R = 10 %
• Compound Amount, A = 1,655

To find

• Principal sum, P =?

Formula required

• Formula for compound Amount

       A = P ( 1 + R/100 )^t

[ Where P is principal sum, R is rate of interest per annum, t is time for interest and A is compound amount ; (Compound Amount = Principal sum + Compound interest) ]

Solution

Using formula to calculate Compound interest

→ A = P( 1 + r/100 )^t  

→ 1655 = P( 1 + 10/100 )^3

→ 1655 = P( 1 + 1/10 )^3

→ 1655 =  P( 1^3 + (1/10)^3 + 3 (1) (1/10) (1 + 1/10) )

→ 1655 = P ( 1 + 1/1000 + 3/10 + 3/100 )

→ 1655 = P ( 1000 + 1 + 300 + 30 ) / 1000

→ 1655 = P ( 1331/1000 )

→ P = 1655 × 1000 / 1331

→ P = 1243.43

Therefore,

• Principal sum would be 1243.43

Answer 2

Question

Find the sum on which the compound interest for 3 years at 10 % per annum amounts to ` 1,655.

Solution

Compound amount = ₹1655

Rate = 10% p.a.

Time = 3yrs

Let, principal be p

ATP

$p(1 + \frac{r}{100})^{3} = 1655 \\ = ) \: p(1 + \frac{10}{100})^{3} = 1655 \\ = ) \: p( \frac{110}{100}) ^{3} = 1655 \\ = ) \: p = 1655 \times \frac{100}{110} \times \frac{100}{110} \times \frac{100}{110} \\ = ) \: p = \frac{165000}{1331} = 1243.426$

Ans:- The principal is ₹1243.426