in this problem: if you wanted to put aside $2,000 a year for 10 years ginven a 10% rate of return (compounded monthly) Here, is it the 10 % every month, or the 10% is divided by 12 months of the year and then every month the % is 0.83%?
In this problem, the 10% rate of return is compounded monthly. This means that the 10% rate is divided by 12 months of the year, and then every month the percentage is 0.83%.
To calculate the value of $2,000 put aside each year for 10 years with a 10% rate of return compounded monthly, you can use the future value of annuity formula.
The formula to calculate the future value of an annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity
P is the periodic payment (in this case, $2,000 per year)
r is the interest rate per period (in this case, 0.83% or 0.0083 as a decimal)
n is the number of periods (in this case, 10 years)
Plugging in the values into the formula, we have:
FV = 2000 * [(1 + 0.0083)^10 - 1] / 0.0083
FV = 2000 * [1.0083^10 - 1] / 0.0083
Calculating this expression will give you the future value of the annuity after 10 years at a 10% compounded monthly rate of return.