Question 1201794: You put $159 per month in an investment plan that pays an APR of 5%. How much money will you have after 24 years? Compare this amount to the total amount of deposits made over the time period.
Found 3 solutions by Theo, math_tutor2020, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 5% compounded monthly = .4166666...% per month.
24 years * 12 months per year = 288 months.
159 invested at the end of each month for 288 months at .4166666.....% per month has a future value of 88,220.19 at the end of the 24 year investment period.
total payments were 159 * 288 = 45,792.
total interest was 88,220.19 minus 45,792 = 42,428.19.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Answers:
future balance = $88,220.19
total deposits = $45,792
Work Shown:
P = 159 = monthly payment
r = 0.05 = APR in decimal form
i = r/12 = 0.05/12 = 0.00416666666666667 approximately = monthly interest rate in decimal form
n = 24*12 = 288 months
We have these inputs
P = 159
i = 0.00416666666666667 (approximately)
n = 288
Compute the future value of the annuity
Use an ordinary annuity and not annuity due.
FV = P*( (1+i)^n - 1 )/i
FV = 159*( (1+0.00416666666666667)^288 - 1 )/0.00416666666666667
FV = 88220.1931150959
FV = 88220.19 dollars will be the account balance after 24 years (aka 288 months)
Let's compare that to what the balance would be if no interest is added.
You deposit $159 per month for 288 months to get 159*288 = 45792 dollars of total deposits.
Subtract the two values marked in red to determine how much more is earned
88220.19 - 45792 = 42428.19
You earn 42,428.19 more dollars if the money is compounded with interest.
Future value annuity calculator
https://www.omnicalculator.com/finance/annuity-future-value
Answer by ikleyn(52921)  (Show Source):
You can put this solution on YOUR website! .
You put $159 per month in an investment plan that pays an APR of 5%.
How much money will you have after 24 years?
Compare this amount to the total amount of deposits made over the time period.
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This problem is posed in a strange way, unprofessionally.
To be professional, the problem should say whether the regular monthly payments
are made: at the beginning of each month or at the end of each month.
Computational procedures are different in these cases, and the answers are different, too.
In my solution, I will assume that the regular monthly payments of $159
are made at the end of each month (ordinary annuity).
Then it is a classic Ordinary Annuity saving plan. The general formula is
FV =  , (1)
where FV is the future value of the account; P is your monthly payment (deposit);
r is the monthly percentage yield presented as a decimal;
n is the number of deposits (= the number of years multiplied by 12, in this case).
Under the given conditions, P = 159; r = 0.05/12; n = 12*24 = 288.
So, according to the formula (1), you get at the end of the 24-th year
FV =  = $88,220.19.
Note that you the deposited amount is only 12*24*159 = $45,792. The rest is what the account earns/accumulates in 24 years.
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On Ordinary Annuity saving plans, see the lessons
- Ordinary Annuity saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
in this site.
The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.
When you learn from these lessons, you will be able to do similar calculations in semi-automatic mode.
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