Answer: 8.38%
Step-by-step explanation:
The formula for interest compounded annually is: [tex]A = P_0(1 + r)^t[/tex] where
- A is the amount accrued (ending balance)
- P₀ is the initial amount invested
- r is the interest rate
- t is the time (in years)
With the given information, we have:
- A = 5P₀
- P₀ = P₀
- r = ?
- t = 20
[tex]5P_0=P_0(1+r)^{20}\\5 = (1+r)^{20}\qquad \qquad \text{divided both sides by}\ P_0\\ln\ 5=ln(1+r)^{20}\\ln\ 5=20\ ln(1+r)\\\\\dfrac{ln\ 5}{20}=ln(1+r)\\\\e^{\frac{ln\ 5}{20}}=e^{ln(1+r)}\\\\e^{\frac{ln\ 5}{20}}=1 + r\\\\e^{\frac{ln\ 5}{20}}-1 = r\\\\0.0838 = r\qquad \rightarrow \qquad 8.38\% = r[/tex]
