Answer:
$1,419.77
Explanation:
To calculate how much you would need to deposit in an account now to have $2,000 in the account in 5 years with a 7% interest rate compounded monthly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future amount you want ($2,000 in this case)
P = the principal amount (the initial deposit you want to calculate)
r = the annual interest rate (7% or 0.07 as a decimal)
n = the number of times the interest is compounded per year (monthly, so n = 12)
t = the number of years (5 in this case)
Now, plug in the values:
$2,000 = P(1 + 0.07/12)^(12 * 5)
First, calculate the values inside the parentheses:
1 + 0.07/12 = 1 + 0.0058333 (rounded to 7 decimal places)
Now, calculate the exponent part:
12 * 5 = 60
So the equation becomes:
$2,000 = P(1.0058333)^60
Now, isolate P:
P = $2,000 / (1.0058333)^60
P ≈ $2,000 / 1.4070419 (rounded to 7 decimal places)
P ≈ $1,419.77 (rounded to the nearest cent)
You would need to deposit approximately $1,419.77 in the account now to have $2,000 in it after 5 years with a 7% interest rate compounded monthly.