peoples bank offers 5% compounded continuously on cds. what amount invested now would grow to $200.000 in 25…

peoples bank offers 5% compounded continuously on cds. what amount invested now would grow to $200.000 in 25 years? hint: solve the continuous compounding formula for p. the present value of $200,000 at 5% compounded continuously for 25 years is approximately $ (round to two decimal places as needed.)

peoples bank offers 5% compounded continuously on cds. what amount invested now would grow to $200.000 in 25 years? hint: solve the continuous compounding formula for p. the present value of $200,000 at 5% compounded continuously for 25 years is approximately $ (round to two decimal places as needed.)

Answer

Explanation:

Step1: Recall the continuous - compounding formula

The formula for continuous compounding is (A = Pe^{rt}), where (A) is the final amount, (P) is the principal (initial amount), (r) is the annual interest rate (in decimal form), and (t) is the time in years. We need to solve for (P), so (P=\frac{A}{e^{rt}}).

Step2: Identify the values of (A), (r), and (t)

Given (A = 20000), (r=0.05) (since (5%= 0.05)), and (t = 25).

Step3: Substitute the values into the formula for (P)

Substitute into (P=\frac{A}{e^{rt}}), we get (P=\frac{20000}{e^{0.05\times25}}). First, calculate the exponent: (0.05\times25 = 1.25). Then (e^{1.25}\approx3.49034296). Now, (P=\frac{20000}{3.49034296}\approx5730.04).

Answer:

(5730.04)