Correct Answer - Option 4 : 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
IA = I × (1 + R/100)t
Here,
IA = 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 (IA) for two years means = (n – 1)year + (n – 2)year
We know that –
IA for (n – 1)year = I × (1 + R/100)t ….. (2)
Put all the given values in equation (2) then we get
IA for (n – 1)year = 7000 × (1 + 10/100)1
⇒ 7000 × (1 + 1/10)
⇒ 7000 × 11/10
⇒ 7700
Now,
IA for (n – 2)year = 4400 × (1 + 10/100)0
⇒ 4400 × 1
⇒ 4400
Now,
Instalment Amount (IA) for two years = 7700 + 4400
⇒ 12100
Now,
We equate the Amount (A) & Instalment Amount (IA)
P × 121/100 = 12100
⇒ P × 1/100 = 100
⇒ P = 100 × 100
⇒ P = 10000
∴ The Sum of the loan will be Rs.10,000