You deposit $5000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years?
To calculate the amount you will have in the account in 30 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest earned
P = the principal investment amount (the initial deposit)
r = the annual interest rate (7% in this case, expressed as a decimal: 0.07)
n = the number of times that interest is compounded per year (since it is compounded annually, n = 1)
t = the number of years the money is invested (30 years in this case)
Plugging in the values, we have:
A = 5000(1 + 0.07/1)^(1*30)
Calculating this equation step by step, we get:
A = 5000(1 + 0.07)^(30)
A = 5000(1.07)^30
A = 5000(2.9775)
A = $14,887.50
Therefore, you will have approximately $14,887.50 in the account after 30 years.
To calculate the amount you'll have in the account in 30 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after time t, including interest
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
In this case, P is $5000, r is 7% (or 0.07 as a decimal), n is 1 (compounded annually), and t is 30 years. Plugging these values into the formula, we get:
A = 5000(1 + 0.07/1)^(1*30)
Calculating the values inside the parentheses:
A = 5000(1.07)^(30)
Using a calculator to raise 1.07 to the power of 30, we get:
A ≈ 5000(2.996727898)
A ≈ $14,983.64
Therefore, after 30 years of depositing $5000 each year into an account earning 7% interest compounded annually, you would have approximately $14,983.64 in the account.