Raju took some loan from a bank at 10% compound interest per annum. He repaid the whole amount of the loan by paying Rs. 7000 and 4400 at the end of the first year and second year respectively. Find the sum of the loan.

Raju took some loan from a bank at 10% compound interest per annum. He repaid the whole amount of the loan by paying Rs. 7000 and 4400 at the end of the first year and second year respectively. Find the sum of the loan. Correct Answer Rs. 10,000

Given:

Rate of interest = 10%

Instalment (I₁) = Rs.7000

Instalment (I₂) = Rs.4400

Time = 2 year

Formula:

A = P × (1 + R/100)ⁿ

Here,

A = Amount

P = Principal Amount

R = Rate of interest

n = time in year

I_A = I × (1 + R/100)^t

Here,

I_A = Instalment Amount

I = Instalment

R = Rate of interest

t = (n – 1)year, (n – 2)year, ……..

Here, n = time in years

Calculation:

Let the principal amount be Rs.P

We know that –

A = P × (1 + R/100)ⁿ  ……. (1)

Put all the given values in equation (1)

A = P × (1 + 10/100)²

⇒ P × (1 + 1/10)²

⇒ P × (11/10)²

⇒ P × 121/100

Now,

Installment Amount (I_A) for two years means = (n – 1)year  +  (n – 2)year

We know that –

I_A for (n – 1)year = I × (1 + R/100)^t ….. (2)

Put all the given values in equation (2) then we get

I_A for (n – 1)year = 7000 × (1 + 10/100)¹

⇒ 7000 × (1 + 1/10)

⇒ 7000 × 11/10

⇒ 7700

Now,

I_A for (n – 2)year = 4400 × (1 + 10/100)⁰

⇒ 4400 × 1

⇒ 4400

Now,

Instalment Amount (I_A) for two years = 7700 + 4400

⇒ 12100

Now,

We equate the Amount (A) & Instalment Amount (I_A)

P × 121/100 = 12100

⇒ P × 1/100 = 100

⇒ P = 100 × 100

⇒ P = 10000