You deposit $2000 in an account earning 7% interest compounded monthly. How much will you have in the account in 10 years?
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You deposit $2000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years?
Well, let's see how your money will grow in a decade. With 7% interest compounded monthly, your account will be blooming like a garden full of money flowers!
First, let's break down the problem. Since you're depositing $2000, that'll be our initial investment. We'll use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money in the account
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time in years
In this case, P = $2000, r = 7% (converted to decimal form, 0.07), n = 12 (monthly compounding), and t = 10.
Let's plug these values into the formula:
A = $2000(1 + 0.07/12)^(12*10)
After shaking our calculations like an overly enthusiastic clown at a birthday party, we find that A ≈ $3,117.49. So, after 10 years, you'll have approximately $3,117.49 in your account!
Wow, isn't compound interest just fabulous? It's like a magic trick that turns your money into more money!
To calculate the amount you will have in the account after 10 years with monthly compounding, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case:
P = $2000
r = 7% = 0.07 (expressed as a decimal)
n = 12 (compounded monthly)
t = 10 years
Substituting these values into the compound interest formula, we have:
A = 2000(1 + 0.07/12)^(12*10)
Now let's calculate it step by step:
Step 1: Calculate (1 + r/n)
(1 + 0.07/12) = 1.0058333 (rounded to 7 decimal places)
Step 2: Calculate (1 + r/n)^(nt)
(1.0058333)^(12*10) ≈ 1.967151 (rounded to 6 decimal places)
Step 3: Calculate A
A = 2000 * 1.967151 ≈ $3,934.30
Therefore, after 10 years with monthly compounding, you will have approximately $3,934.30 in the account.