Suppose you deposit $10,000 into a savings account with 3.5% compound interest compounded each month. Find the account balance in 50 years. Round the answer to the nearest thousand dollars.
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(starting amount) * [1 + (interest per compounding)]^(compoundings)
10,000 * [1 + (.035 / 12)]^(12 * 50)
P = Po(1+r)^n,
r = 0.035/12 = 0.00292 = monthly % rate expressed as a decimal,
n = 12comp./yr. * 50yrs. = 600 compounding periods,
P = 10,000(1.00292)^600 =
To find the account balance in 50 years with compound interest, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the account balance after t years
P = the initial deposit or principal amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case:
P = $10,000
r = 3.5% or 0.035 (as a decimal)
n = 12 (compounded monthly)
t = 50 years
Substituting these values into the formula, we get:
A = 10,000(1 + 0.035/12)^(12*50)
Calculating this, we get:
A ≈ 10,000(1 + 0.0029)^(600)
A ≈ 10,000(1.0029)^(600)
A ≈ 10,000(1.972060)
A ≈ 19,720.60
Rounding the answer to the nearest thousand dollars, the account balance after 50 years is approximately $19,721.
Please note that this is an approximation, and the actual account balance may vary slightly due to rounding or other factors.