Question

A sum of Rs. 12200 is to be repaid in three equal annual installments. If the rate of interest is 25%, compounded annually, then the value of each installment?

1. Rs. 6450
2. Rs. 5950
3. Rs. 6600
4. Rs. 6250
5. None of these

Answer 1

Correct Answer - Option 4 : Rs. 6250

Given:

Principal Amount = Rs.12200

Rate of interest = 25%

Three equal annual instalment means (Time) = 3 years

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:

We know that –

A = P × (1 + R/100)ⁿ  ……. (1)

Put all the given values in equation (1)

A = 12200 × (1 + 25/100)³

⇒ 12200 × (1 + 1/4)³

⇒ 12200 × (5/4)³

⇒ 12200 × 125/64

Now,

Let the instalment be Rs.y

Instalment Amount (I_A) for three years means = (n – 1)year  +  (n – 2)year +(n – 3)year

We know that –

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

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

I_A for (n – 1)year = y × (1 + 25/100)²

⇒ y × (1 + 1/4)²

⇒ y × (5/4)²

⇒ 25y/16

Similarly,

I_A for (n – 2)year = y × (1 + 25/100)¹

⇒ y × (1 + ¼)

⇒ y × 5/4

⇒ 5y/4

Now,

I_A for (n – 3)year = y × (1 + 25/100)⁰

⇒ y × 1

⇒ y

Instalment Amount (I_A) for three years = 25y/16 + 5y/4 + y

⇒ (25y +20y + 16y)/16

⇒ 61y/16

Now,

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

12200 × 125/64 = 61y/16

⇒ 200 × 125/4 = y

⇒ y = 50 × 125

⇒ y = 6250

∴ The Value of each instalment will be Rs.6250