A deposit of 50,000 SEK grows at 3% annual compound interest. How many years are required for the balance to surpass 65,000 SEK? (log(1.3) approx 0.1139, log(1.03) approx 0.0128)
Answer and explanation
Correct answer: A. 9 years
- Step 1: Set up the inequality: 50000 (1.03)^t > 65000 => (1.03)^t > 1.3. Step 2. Take logarithms: t log(1.03) > log(1.3). Step 3. Solve for t: t > 0.1139 / 0.0128 approx 8.898 years. Step 4. Since interest is credited annually, 9 years are needed. Answer: 9 years. Why not the others: 8 years yields approx 63,338 SEK, which is below 65,000 SEK; 10 years is not the minimum full year.
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