EMI = $1,264.44

UpStudy Free Step by Step Solution:

To calculate the monthly mortgage payments, we use the formula for the monthly payment of a fixed-rate mortgage:

\[M = \frac { P \cdot r \cdot ( 1 + r) ^ n} { ( 1 + r) ^ n - 1} \]

Where:

- \(M\)is the monthly payment

- \(P\) is the loan principal (the amount borrowed)

- \(r\) is the monthly interest rate (annual interest rate divided by 12)

- \(n\) is the total number of payments (loan term in years multiplied by 12)

Given:

- The apartment price is R151,000

- The down payment is R51,000

- The loan principal \(P\) = R151,000 - R51,000 = R100,000

- The annual interest rate is 15%, so the monthly interest rate \(r\) = 15% / 12 = 0.15 / 12 = 0.0125

- The loan term is 30 years, so the total number of payments \(n\) = 30 * 12 = 360

Plugging these values into the formula:

\[ M = \frac{100,000 \cdot 0.0125 \cdot (1 + 0.0125)^{360}}{(1 + 0.0125)^{360} - 1} \]

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Key Concepts:

1. Fixed-Rate Mortgage: A mortgage with a constant interest rate and monthly payments that never change throughout the loan term.

2. Monthly Payment Formula: The formula used to calculate the monthly payment on a fixed-rate mortgage is:

\(M = \frac { P \cdot r \cdot ( 1 + r) ^ n} { ( 1 + r) ^ n - 1} \)

where \(M\) is the monthly payment, \(P\) is the loan principal, \(r\) is the monthly interest rate, and \(n\) is the total number of payments.

Understanding these principles makes it possible to calculate the mortgage payment per month, which is required to come up with financial plans and manage different loans properly. For more help with a step-by-step way to calculate your mortgage loan—or just about any other financial concept—use the UpStudyAI Homework Solver. With superior explanations and individually responsive support, UpStudy ensures that you have been availed with enough knowledge on every subject, therefore making you one of the best in that field. Experience UpStudy today!