The correct option is this 10.51 years.
In Finance MCQs, calculating the time required for an investment to reach a specific financial target is a crucial application of the time value of money (TVM) concept. This concept emphasizes that money available...
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The correct option is this 10.51 years.
In Finance MCQs, calculating the time required for an investment to reach a specific financial target is a crucial application of the time value of money (TVM) concept. This concept emphasizes that money available today is worth more than the same amount in the future due to its potential earning capacity. Compounding allows investments to grow over time by earning interest not only on the principal but also on accumulated interest from prior periods. Understanding how to determine the number of periods required for an investment to grow to a desired amount is therefore essential for finance students, analysts, and investors.
In this problem, we are tasked with determining how many years it will take for Rs. 6,000 to grow to Rs. 10,000 at an annual interest rate of 5% compounded annually. The fundamental formula applied here is the future value of a single sum with annual compounding:
FV=PV×(1+r)n
Where:
FV = Future Value (Rs. 10,000)
PV = Present Value (Rs. 6,000)
r = Annual interest rate (5% or 0.05)
n = Number of years
Since we are solving for nnn, we need to rearrange the formula using logarithms, as the exponent is unknown:
n=ln(1+r)ln(FV/PV)
Substituting the given values:
n=ln(1+0.05)ln(10,000/6,000)=ln(1.05)ln(1.6667)≈0.048790.5108≈10.51 years
Thus, it will take approximately 10.51 years for Rs. 6,000 to grow to Rs. 10,000 at a 5% annual interest rate with yearly compounding.
Understanding this calculation is critical in finance MCQs because it tests several interrelated skills:
Application of the compound interest formula – knowing how to set up the equation for future value.
Algebraic manipulation and logarithms – being able to solve for the unknown exponent in a growth equation.
Financial reasoning – interpreting the result in the context of investment planning.
The other options in typical MCQs are intentionally misleading:
8.42 years underestimates the time because it ignores the compounding effect over multiple periods.
15.75 or 18.78 years overestimate the required time, reflecting a misunderstanding of exponential growth and logarithmic calculation.
This type of problem has both academic and practical significance. In personal finance, investors use this skill to plan for retirement, save for education, or achieve specific wealth goals. Financial planners often reverse-engineer compounding to determine how long clients need to invest to meet target sums at assumed rates of return. It also reinforces the principle of compound interest, which is one of the most powerful concepts in finance, as it allows money to grow faster over time compared to simple interest.
Additionally, mastery of this concept strengthens problem-solving skills for competitive exams, banking tests, CFA or ACCA modules, and other finance certifications. Questions like this also teach students how to think critically about investment horizons, rates of return, and the impact of time on wealth accumulation.
Conclusion:
By carefully applying the compound interest formula and logarithms, we can conclude that it will take approximately 10.51 years for Rs. 6,000 to grow to Rs. 10,000 at 5% annual interest compounded annually. Mastering such calculations equips finance students, professionals, and investors to understand the time value of money, plan investments effectively, and confidently answer Finance MCQs related to compounding, future value, and investment planning.
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