Question

You would like to have $1,000,000 in 33 years by making regular deposits at the end of each month in an annuity that pays 7% compounded monthly. Determine the deposit at the end of each month. Do not round until the final answer. Then round to the nearest dollar as needed.

Answer 1

Okay, I have attached the formula for solving the monthly amount of a monthly annuity.

Answer 2

To use the formula the time is the number of months +1 and the rate = the (annual rate / 12)

Monthly Amount = 1,000,000 /({ [(1.0058333333)^397 -1]/.0058333333 } -1)
Monthly Amount = 1,000,000 / {[(10.065411803 -1) / .0058333333]-1}
Monthly Amount = 1,000,000 / ((9.065411803 / .0058333333)-1)
Monthly Amount = 1,000,000 / (1,554.0705948003 -1)
Monthly Amount = 1,000,000 / 1,553.0705948003
Monthly Amount = 643.89

Here's a monthly annuity calculator to check the calculations
http://1728.org/annuitym.htm

Then again it should be interest compounded monthly.

Answer 3

7 per cent interest compounded annually =
7.229008086 compounded monthly
monthly rate = 7.229008086 / 1200 =
0.0060241734

Monthly Amount=1,000,000 /({ [(1.0060241734)^397 -1] / .0060241734}-1)
Monthly Amount=1,000,000 /({ [10.8527873492 -1) / .0060241734}-1)
Monthly Amount=1,000,000 / ({[9.8527873492] / .0060241734}-1)
Monthly Amount=1,000,000 / ({1,635.5417891822}-1)
Monthly Amount=1,000,000 / ({1,634.5417891822})
Monthly Amount=611.79
And you can check this amount with the annuity calculator
http://1728.org/annuitym.htm
Just remember to put 7.229008086 in the yearly rate input box.