The correct option is this 12 years.
In Finance MCQs, calculating the loan repayment period is a key application of the time value of money (TVM) concept. This problem illustrates an amortized loan, where equal annual payments are made to fully...
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The correct option is this 12 years.
In Finance MCQs, calculating the loan repayment period is a key application of the time value of money (TVM) concept. This problem illustrates an amortized loan, where equal annual payments are made to fully repay a loan including both principal and interest over a specific period. Understanding this calculation is crucial for students, analysts, and finance professionals because it reflects real-world scenarios such as mortgages, car loans, business loans, and corporate financing.
The borrower takes a loan of Rs. 11,000 at an annual interest rate of 5%, with equal yearly payments of Rs. 1,241.08. To determine how long it will take to fully repay this loan, we use the present value of an annuity formula:
Loan Amount=Payment×Present Value Interest Factor of Annuity (PVIFA)
Here, the PVIFA accounts for the interest applied over multiple periods, reflecting how each payment is split between interest and principal. To estimate the number of years:
PVIFA=Annual PaymentLoan Amount=1,241.0811,000≈8.86
Using a PVIFA table at 5% interest, the value closest to 8.86 corresponds to 12 years, indicating that the loan will be repaid over 12 annual installments.
This calculation emphasizes the relationship between interest rates, payment amounts, and loan duration:
Loan Amount – Higher principal requires either larger payments or longer repayment periods.
Interest Rate – A higher interest rate increases the total interest portion in each installment, extending the repayment period if payments remain constant.
Payment Size – Increasing the annual payment reduces the repayment period because more principal is covered each year.
The principle behind this is the time value of money: a rupee today is worth more than a rupee tomorrow because it can earn interest. In an amortized loan, part of each payment covers interest, while the remainder reduces the principal. Early payments consist largely of interest, while later payments increasingly reduce principal, illustrating the dynamic allocation of cash flows over time.
Why the other options are incorrect:
6 years – Too short. This would require significantly larger payments than Rs. 1,241.08.
24 years – Too long. This implies very small payments relative to the loan size.
48 years – Far too long. A loan of Rs. 11,000 at 5% cannot be repaid over 48 years with Rs. 1,241.08 annual payments.
Understanding loan amortization is practical because it informs financial planning, debt management, and investment decisions. Analysts often prepare amortization schedules, which detail the principal and interest breakdown of each payment. These schedules are essential for businesses and individuals to track outstanding obligations, forecast cash flows, and plan for early repayment strategies.
From an educational standpoint, this type of Finance MCQ helps students:
Apply present value and annuity formulas effectively.
Understand the impact of interest rates on repayment schedules.
Analyze real-life financial scenarios such as personal loans, corporate debt, and project financing.
In conclusion, using the present value of annuity concept at a 5% annual interest rate, the correct loan repayment period is 12 years. Mastering this method allows finance students, analysts, and professionals to calculate amortization schedules accurately, interpret loan obligations, and confidently answer Finance MCQs related to the time value of money. This understanding also equips them to make informed financial decisions in personal finance, corporate finance, and investment management.
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