Question 1136750: AT AGE 25, TO SAVE FOR RETIREMENT, YOU DECIDE TO DEPOSIT $75 INTO AN IRA AT THE END OF EACH MONTH AT AN INTEREST RATE OF 6.5% PER YEAR COMPOUNDED DAILY. HOW MUCH WILL YOU HAVE FROM THE IRA WHEN YOU RETIRE AT AGE 65? FIND THE INTEREST.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you meant compounded monthly, it's pretty straight forward with the use of a financial calculator.
if you meant compounded daily, it becomes more complex, but can still be done.
first i'll do compounded monthly.
next i'll do compounded daily.
the interest is the future value minus the sum of the payments.
480 * 70 = total payments of 33,600.
with monthly compounding, the interest is the future value minus the sum of the payments = 159,853.32 - 33,600 = 126,253.32.
with daily compounding, the interest is the future value minus the sum of the payments = 160,608.18 - 33,600 = 127,018.18
with monthly compounding the annual rate of 6.5% is divided by 12 to get a monthly rate of .541666666666.....
with daily compounding, there are probably several methods to calculate it.
not knowing which method your instructor might have wanted you to use, the method i chose is the following.
6.5 / 365 = a daily rate percent of .0178082192.
divide that by 100 to get a daily rate of .000178082192.
add 1 to it to get 1.000178082192.
that's the daily rate plus 1.
to convert it to a monthly rate plus 1, do the following:
1.000178082192 ^ (365 / 12) = 1.005430878.
that's the monthly rate plus 1.
subtract 1 from that to get .005430878.
that's the monthly rate.
multiply that by 100 to get .5430878.
that's the monthly rate percent that is input into the calculator.
the rate percents shown in the calculator are the figures i gave you rounded to 6 decimal digits.
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