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PLEASE HELP ASAP!

How much would you have to deposit in
an account with a 4.75% interest rate,
compounded continuously, to have
$20,000 in your account 20 years later?
P = $[?]
Round to the nearest cent.

PLEASE HELP ASAP! How much would you have to deposit in an account with a 4.75% interest-example-1
User Henry Yang
by
7.4k points

1 Answer

7 votes

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

User Gams Basallo
by
7.6k points