In a lifetime mortgage of €100,000 at 5.5% with no payments, how many years would it take for the loan outstanding to double?

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Enhance your understanding of financial advising with the Qualified Financial Adviser (QFA) Loans Exam 1 Test. Prepare with detailed questions, hints, and explanations to ace your exam!

Multiple Choice

In a lifetime mortgage of €100,000 at 5.5% with no payments, how many years would it take for the loan outstanding to double?

Explanation:
With no payments, the loan balance grows each year by the annual interest rate. After t years, the balance is 100,000 × (1.055)^t. To double the loan, set this equal to 200,000 and solve for t: (1.055)^t = 2. Take natural logs: t = ln(2) / ln(1.055) ≈ 0.6931 / 0.0535 ≈ 12.97 years, about 13 years. This matches the quick rule of thumb: doubling time ≈ 72 / 5.5 ≈ 13.1 years. So it takes roughly thirteen years for the balance to double at 5.5% with no payments. Shorter times would require higher effective growth (e.g., five years would need a rate around 9–10%), which isn’t the case here.

With no payments, the loan balance grows each year by the annual interest rate. After t years, the balance is 100,000 × (1.055)^t. To double the loan, set this equal to 200,000 and solve for t: (1.055)^t = 2. Take natural logs: t = ln(2) / ln(1.055) ≈ 0.6931 / 0.0535 ≈ 12.97 years, about 13 years.

This matches the quick rule of thumb: doubling time ≈ 72 / 5.5 ≈ 13.1 years. So it takes roughly thirteen years for the balance to double at 5.5% with no payments. Shorter times would require higher effective growth (e.g., five years would need a rate around 9–10%), which isn’t the case here.

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