I will deposit $1000 per year for 25 years.� Assuming a 5% compound interest rate, what will my account be worth in 25 years? �Now assume a 10% compound rate and calculate my future balance
After 25 years, 26 deposits of $1000 will have been made, but the last deposit will not have earned interest. The amount accumulated with annually compounded interest after n years at interest rate r, with annual deposits of x, is
x [(1 + r)^(n+1) - 1]/r
With x = 1000, r = 0.05 and n = 25,
Balance = 1000[1.05)^26 -1].05
= $51,113.45
At 10% interest, it becomes $109,181.77
To calculate the future balance of your account over 25 years, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = the future balance of the account
P = the annual deposit amount
r = the interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
For the first scenario, with a 5% compound interest rate:
P = $1000
r = 5% = 0.05
n = 1 (since the interest is compounded annually)
t = 25
Plug in these values into the formula:
A = $1000 * (1 + 0.05/1)^(1*25)
A = $1000 * (1 + 0.05)^25
A = $1000 * (1.05)^25
Now, let's calculate the future balance using a calculator or spreadsheet:
A = $1000 * (1.05)^25
A ≈ $3386.97
Therefore, your account is expected to be worth approximately $3386.97 after 25 years.
For the second scenario, with a 10% compound interest rate:
P = $1000
r = 10% = 0.10
n = 1 (since the interest is compounded annually)
t = 25
Plug in these values into the formula:
A = $1000 * (1 + 0.10/1)^(1*25)
A = $1000 * (1 + 0.10)^25
Now, let's calculate the future balance using a calculator or spreadsheet:
A = $1000 * (1.10)^25
A ≈ $10834.71
Therefore, your account is expected to be worth approximately $10834.71 after 25 years with a 10% compound interest rate.