I can only put away $2,000 a year. I am 25 and plan on retiring at 65 and earning 5%. How much will I have in 40 years?
amount = 2000 ( 1.05^40 - 1)/.05
= ....
To calculate how much you will have in 40 years, we'll need to use the compound interest formula. The formula is:
A = P*(1+r/n)^(n*t)
Where:
A = the final amount or future value
P = the principal amount or initial investment
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Let's plug in the values you provided:
P = $2,000 (annual deposit)
r = 5% (annual interest rate, which is 0.05 as a decimal)
n = 1 (interest compounded annually)
t = 40 (number of years)
We can now calculate the future value (A):
A = $2,000 * (1 + 0.05/1)^(1*40)
A = $2,000 * (1 + 0.05)^40
A = $2,000 * (1.05)^40
Using a calculator, we find that (1.05)^40 is approximately 7.0408. Therefore:
A = $2,000 * 7.0408
A ≈ $14,081.60
So, if you put away $2,000 per year for 40 years with a 5% annual interest rate, you would have approximately $14,081.60 at the end of the 40-year period.
To calculate the future value of your savings over 40 years, we can use the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate)^Number of Periods
Given that you can save $2,000 per year, the present value would be $2,000. The interest rate is 5%, which can be converted to 0.05 as a decimal. The number of periods is 40 (years).
Plugging these values into the formula:
Future Value = $2,000 * (1 + 0.05)^40
Calculating this equation:
Future Value = $2,000 * (1.05)^40
Future Value = $2,000 * 4.32194
Therefore, you will have approximately $8,643.88 after 40 years of saving $2,000 per year with an annual interest rate of 5%.