You deposit $4000 in an account earning 5% interest compounded monthly. How much will you have in the account in 5 years?


Use n=12 for monthly compounding,n=4 for quarterly compounding,n=2 for semiannual compounding, and n=1 for annual compounding.)

200

Well, let me calculate that for you while I juggle these numbers.

With monthly compounding (n=12), you'll have $4,000 growing at a rate of 5% per year, divided by 12. So, in 5 years, you'll have... *drumroll, please*... approximately $4,537.03 in your account.

But wait, there's more! If we switch it up a bit and go for quarterly compounding (n=4), you'll have... ta-da!... around $4,536.42 in your account after 5 years. Just a tad less, but still a pretty penny!

Now, let's try semiannual compounding (n=2). Get ready for the grand reveal... You'll have an estimated whopping amount of $4,535.97 in your account after 5 years. Almost there!

And finally, let's go for the gold with annual compounding (n=1). The suspense is killing me... In 5 years, you'll have an impressive sum of... $4,524.63 in your account.

So, my friend, with these different compounding options, you can see that the amount in your account varies slightly, but no matter what, your money will be makin' moves!

To calculate the amount you will have in the account in 5 years with an interest rate of 5% compounded monthly, we will use the formula for compound interest:

A = P(1+r/n)^(n*t)

Where:
A = the amount you will have in the account after t years
P = the initial principal amount (the amount you deposited) which is $4000 in this case
r = annual interest rate, which is 5%
n = number of times the interest is compounded per year, which is 12 for monthly compounding
t = number of years, which is 5 in this case

Plugging in the values into the formula, we have:

A = 4000(1+(0.05/12))^(12*5)

Now, let's calculate step by step.

Step 1: Calculate the monthly interest rate:
r Monthly = r/n = 0.05/12 = 0.004167

Step 2: Calculate the number of compounding periods:
n*t = 12*5 = 60

Step 3: Calculate the amount in the account after 5 years:
A = 4000(1+0.004167)^(60)

Calculating, we find:

A ≈ 4000(1.004167)^(60)

A ≈ 4000(1.281503205)

A ≈ 5126.01

Therefore, you will have approximately $5126.01 in the account after 5 years with monthly compounding at an interest rate of 5%.

To calculate the future value of an account with compounded interest, we can use the formula:

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

Where:
A = future value of the account
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of compounding periods per year
t = number of years

In this case:
P = $4000
r = 5% = 0.05
n = 12 (since interest is compounded monthly)
t = 5 years

Substituting these values into the formula, we get:

A = $4000(1 + 0.05/12)^(12*5)

Now, let's calculate the future value using a calculator or spreadsheet:

A = $4000 * (1 + 0.05/12)^(12*5)
A ≈ $4,033.25

Therefore, after 5 years, you would have approximately $4,033.25 in the account.

4000 * [1 + (.05 / 12)]^(5 * 12)