How much would you have to deposit in
an account with a interest rate,
compounded continuously, to have
in your account 8 years later?

Round to the nearest cent.

Ask by Medina Mcdonald. in the United States

Jan 21,2025

Question

How much would you have to deposit in
an account with a interest rate,
compounded continuously, to have
in your account 8 years later?

Round to the nearest cent.

Ask by Medina Mcdonald. in the United States

Jan 21,2025

UpStudy AI · Accepted Answer

To determine the initial deposit $$ P $$ needed to have \$2,500 in your account after 8 years with a continuously compounded interest rate of $$ 7.5\% $$, you can use the formula for continuous compounding:

$$
A = P e^{rt}
$$

Where:
- $$ A $$ is the amount of money accumulated after $$ t $$ years (\$2,500),
- $$ P $$ is the principal amount (initial deposit),
- $$ r $$ is the annual interest rate (7.5% or 0.075),
- $$ t $$ is the time the money is invested for (8 years),
- $$ e $$ is the base of the natural logarithm (approximately 2.71828).

Rearranging the formula to solve for $$ P $$:

$$
P = \frac{A}{e^{rt}}
$$

Plugging in the known values:

$$
P = \frac{2500}{e^{0.075 \times 8}} = \frac{2500}{e^{0.6}}
$$

First, calculate $$ e^{0.6} $$:

$$
e^{0.6} \approx 1.8221188
$$

Now, divide \$2,500 by this value:

$$
P \approx \frac{2500}{1.8221188} \approx 1372.03
$$

**Rounded to the nearest cent:**

$$
P = \$1,\!372.03
$$
You need to deposit \$1,372.03 initially to have \$2,500 after 8 years with a 7.5% continuously compounded interest rate.

How much would you have to deposit in
an account with a interest rate,
compounded continuously, to have
in your account 8 years later?

Round to the nearest cent.

Upstudy AI Solution

Answer

Solution

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How much would you have to deposit in an account with a interest rate, compounded continuously, to have in your account 8 years later? Round to the nearest cent.

Upstudy AI Solution

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How much would you have to deposit in
an account with a interest rate,
compounded continuously, to have
in your account 8 years later?

Round to the nearest cent.