what is the future value of $490 per year for ten years compounded annually at 11%
To calculate the future value of $490 per year for ten years compounded annually at 11%, you can use the formula for the future value of an annuity:
Future Value = Payment x [((1 + Interest Rate)^Number of Periods) - 1] / Interest Rate
In this case:
Payment = $490
Interest Rate = 11% = 0.11 (expressed as a decimal)
Number of Periods = 10 years
Now, let's substitute the values into the formula and calculate the future value:
Future Value = $490 x [((1 + 0.11)^10) - 1] / 0.11
Calculating the expression within the brackets [((1 + 0.11)^10) - 1]:
[(1 + 0.11)^10] = 1.11^10 = 1.710502882
[1.710502882 - 1] = 0.710502882
Substituting back into the formula:
Future Value = $490 x 0.710502882 / 0.11
Future Value = $3,070.45
Therefore, the future value of $490 per year for ten years compounded annually at 11% is approximately $3,070.45.