Answer: you would need to deposit approximately $7,710.07 in the account to have $20,000 after 20 years, rounding to the nearest cent
Explanation:
To calculate the amount you would need to deposit in an account with a 4.75% interest rate, compounded continuously, to have $20,000 in your account 20 years later, you can use the formula for continuous compound interest:
A = Pe^(rt)
Where:
A = the future value of the investment
P = the initial deposit
e = Euler's number, approximately 2.71828
r = the interest rate (in decimal form)
t = the time period (in years)
In this case, you want to find the initial deposit, so you can rearrange the formula as follows:
P = A / e^(rt)
Plugging in the given values:
A = $20,000
r = 4.75% = 0.0475 (convert to decimal)
t = 20 years
P = $20,000 / e^(0.0475 * 20)
Using a calculator, you can find the value of e^(0.0475 * 20) ≈ 2.71828^(0.0475 * 20) ≈ 2.71828^0.95 ≈ 2.59374
Therefore, the initial deposit P would be:
P = $20,000 / 2.59374 ≈ $7,710.07
So, you would need to deposit approximately $7,710.07 in the account to have $20,000 after 20 years, rounding to the nearest cent