lamonte is going to invest in an account paying an interest rate of 4% compounded continuously. how much…

lamonte is going to invest in an account paying an interest rate of 4% compounded continuously. how much would lamonte need to invest, to the nearest cent, for the value of the account to reach $12,300 in 8 years?

lamonte is going to invest in an account paying an interest rate of 4% compounded continuously. how much would lamonte need to invest, to the nearest cent, for the value of the account to reach $12,300 in 8 years?

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 investment), (r) is the annual interest rate (in decimal form), and (t) is the time in years. Given (A=$12300), (r = 0.04), and (t = 8). We need to solve for (P). From (A = Pe^{rt}), we can rewrite it as (P=\frac{A}{e^{rt}}).

Step2: Substitute the values into the formula

Substitute (A = 12300), (r=0.04), and (t = 8) into (P=\frac{A}{e^{rt}}). First, calculate (rt): (rt=0.04\times8 = 0.32). Then, (e^{rt}=e^{0.32}\approx1.3771277). Now, (P=\frac{12300}{e^{0.32}}=\frac{12300}{1.3771277}).

Step3: Calculate the value of (P)

(P=\frac{12300}{1.3771277}\approx8932.96)

Answer:

(8932.96)