A tax free municipal bond pays 4.75% compounded continuously. What is the value of a $2,000 bond after 30 years? Round your answer to the nearest cent.
[Hint- A=P e^rt where P= present(initial) value, A= future value, r= annual rate, and t= number of years]
P.S.The rt is an exponent to e
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2306.306162
To calculate the future value of a tax-free municipal bond, we can use the formula:
A = P * e^(rt),
where A represents the future value, P is the present value (initial investment), r is the annual interest rate, and t is the number of years.
In this case, we are given the following information:
- Present value (P): $2,000
- Annual interest rate (r): 4.75%
- Number of years (t): 30
Now, let's substitute these values into the formula:
A = 2000 * e^(0.0475 * 30).
First, we need to calculate the exponent part: 0.0475 * 30 = 1.425.
Next, we substitute this result into the formula:
A = 2000 * e^(1.425).
Using a scientific calculator or an online exponential calculator, we can evaluate e^(1.425), which is approximately 4.1552.
Finally, we multiply this result by $2,000:
A = 2000 * 4.1552 = $8,310.40 (rounded to the nearest cent).
Therefore, after 30 years, the value of the $2,000 tax-free municipal bond would be approximately $8,310.40.