Question

You deposit $5000 in an account earning 5% interest compounded monthly. How much will you have in the account in 15 years?

Answer 1

Answer: 9,737.29

Step-by-step explanation:

A = P(1 + r/n)^(nt)

Where:

A is the future value of the account,

P is the initial deposit ($5000),

r is the annual interest rate (5% or 0.05),

n is the number of times the interest is compounded per year (12 for monthly compounding), and

t is the number of years (15).

Using this formula, we can calculate the future value as follows:

A = 5000(1 + 0.05/12)^(12*15)

First, let's simplify the calculation inside the parentheses:

1 + 0.05/12 = 1.0041667 (rounded to 7 decimal places)

Now, let's substitute the values into the formula:

A = 5000(1.0041667)^(12*15)

Next, calculate the exponent:

12*15 = 180

Now, let's raise the simplified value to the power of 180:

A = 5000(1.0041667)^180

Using a calculator or spreadsheet, you can find that (1.0041667)^180 ≈ 1.9474573.

Finally, multiply the initial deposit by the result to find the future value:

A = 5000 * 1.9474573

A ≈ $9,737.29

Answer 2

The final amount in the account after 15 years, with an initial deposit of $5000 and a 5% interest rate compounded monthly, is approximately $9358.19.

Step-by-step explanation:

To calculate the amount of money in the account after 15 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount
• P is the principal amount (initial deposit)
• r is the annual interest rate (in decimal form)
• n is the number of times interest is compounded per year
• t is the number of years

In this case, we have:

• P = $5000
• r = 5% = 0.05
• n = 12 (compounded monthly)
• t = 15

Plugging in these values, we get:

A = $5000(1 + 0.05/12)^(12*15) = $9358.19

So, after 15 years, you will have approximately $9358.19 in the account.