Mr. Rajan has taken a loan of Rs. 3,00,000 from a commercial bank at 7.5% p.a. rate of interest. He has to repay it in 6 equal annual installments. Determine the size of a single installment.

Mr. Rajan has taken a loan of Rs. 3,00,000 from a commercial bank at 7.5% p.a. rate of interest. He has to repay it in 6 equal annual installments. Determine the size of a single installment. 

To determine the size of a single installment for repaying the loan, we can use the formula for calculating the equal installment of a loan, also known as an "annuity" formula. The formula is:

$�\mathrm{<span\; style="font-size:\; 1.21em;"><span\; style="font-family:\; KaTeX\_Main,\; Times\; New\; Roman,\; serif;">�</span></span>}\mathrm{<span\; style="font-size:\; 1.21em;"><span\; style="font-family:\; KaTeX\_Main,\; Times\; New\; Roman,\; serif;">�</span></span>}<span\; style="font-size:\; 1.21em;"><span\; style="font-family:\; KaTeX\_Main,\; Times\; New\; Roman,\; serif;">=</span></span>\frac{}{}$�×�×(1+�)�(1+�)�−1

Where:

• $���$ is the equal annual installment,
• $�$ is the principal amount (loan amount),
• $�$ is the interest rate per period (expressed as a decimal), and
• $�$ is the number of periods (in this case, the number of installments).

Given:

• Principal amount ($�$) = Rs. 3,00,000
• Interest rate ($�$) = 7.5% per annum = 0.075 (when expressed as a decimal)
• Number of installments ($�$) = 6

Substitute these values into the formula:

$���=\frac{3,00,000\times 0.075\times (1+0.075{)}^6}{(1+0.075{)}^6-1}$

Calculate the value of $���$:

$���=\frac{3,00,000\times 0.075\times 1.546981\dots }{1.546981\dots -1}$

$���=\frac{35,000.9\dots }{0.546981\dots }$

$���\approx 64,005.84$

So, the size of a single installment (equal annual installment) that Mr. Rajan needs to pay is approximately Rs. 64,005.84.

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