Step-by-Step Solution

Topic: Financial Mathematics (EMI)

Given Parameters

• • Principal (P) = ₹ 30,00,000
• • Annual Rate (R) = 7.5% p.a.
• • Monthly Rate (i) = 7.5 / (12 * 100) = 0.00625
• • Time (n) = 20 years * 12 = 240 months
• • Given Value: (1.00625)²⁴⁰ = 4.4608

(I) CALCULATE EMI

Formula: EMI = P * i * [ (1+i)ⁿ / ( (1+i)ⁿ – 1 ) ]

Substitute values:

EMI = 3000000 * 0.00625 * [ 4.4608 / (4.4608 – 1) ]

EMI = 18750 * [ 4.4608 / 3.4608 ]

EMI = 18750 * 1.28895…

(Rounding to nearest Rupee: ₹ 24,168)

(II) PRINCIPAL IN 150th INSTALMENT

Formula for Principal portion in k-th instalment:

P_k = EMI * (1+i)^-(n-k+1)

Here k = 150. So, n – k + 1 = 240 – 150 + 1 = 91.

We need (1.00625)^-91 = 1 / (1.00625)⁹¹

Given (1.00625)⁹¹ = 1.7629.

P₁₅₀ = 24167.81 * (1 / 1.7629)

P₁₅₀ = 24167.81 / 1.7629

(III)(A) TOTAL INTEREST PAID

Total Payment = EMI * Number of Instalments (n)

Total Payment = 24167.81 * 240 = ₹ 58,00,274.40

Total Interest = Total Payment – Principal Loan Amount

Total Interest = 58,00,274.40 – 30,00,000

(III)(B) TOTAL AMOUNT PAID

The total amount paid to repay the loan is simply the sum of all EMIs paid over the tenure.

Total Amount = EMI * n

Total Amount = 24167.81 * 240