QuestionJuly 27, 2025

Simon wants to invest 5,000 and increase the investment to 10,000 If the money earns 5.4% compounded annually, approximately how long will it take Simon to meet his goal? 5 and a half years 10 years 13 years 21 years

Simon wants to invest 5,000 and increase the investment to 10,000 If the money earns 5.4% compounded annually, approximately how long will it take Simon to meet his goal? 5 and a half years 10 years 13 years 21 years
Simon wants to invest 5,000 and increase the investment to 10,000 If the money earns 5.4% compounded annually, approximately how long will it take Simon to meet his goal? 5 and a half years 10 years 13 years 21 years

Solution
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Answer

13 years Explanation 1. Use the compound interest formula The formula is A = P(1 + r)^t, where A is the amount, P is the principal, r is the rate, and t is the time. 2. Set up the equation 10,000 = 5,000(1 + 0.054)^t 3. Solve for t Divide both sides by 5,000: 2 = (1.054)^t Take the logarithm of both sides: \log(2) = t \cdot \log(1.054) Solve for t: t = \frac{\log(2)}{\log(1.054)} 4. Calculate t Using a calculator, t \approx \frac{0.3010}{0.0223} \approx 13.49

Explanation

1. Use the compound interest formula<br /> The formula is $A = P(1 + r)^t$, where $A$ is the amount, $P$ is the principal, $r$ is the rate, and $t$ is the time.<br />2. Set up the equation<br /> $10,000 = 5,000(1 + 0.054)^t$<br />3. Solve for $t$<br /> Divide both sides by $5,000$: $2 = (1.054)^t$<br /> Take the logarithm of both sides: $\log(2) = t \cdot \log(1.054)$<br /> Solve for $t$: $t = \frac{\log(2)}{\log(1.054)}$<br />4. Calculate $t$<br /> Using a calculator, $t \approx \frac{0.3010}{0.0223} \approx 13.49$
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