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Calculate the present value for the annuities listed below.
You want to be paid $200 every month for 30 months. The interest rate is 6%/ compounded monthly.
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Use the general formula A = .
Here A is the initial amount at the account ("present value");
W is the monthly withdrawn value; r is the monthly percentage r = 0.06/12, presented as a decimal;
p = 1 + r and n is the number of withdrawing periods (months, in this case).
The formula assumes that withdraws are made at the beginning of every month, starting from the opening the account.
In this problem, W = 200 dollars; the monthly rate is r = 0.06/12 = 0.005, p = 1 + 0.005 = 1.005,
the number of payment periods (= the number of months) is n = 30. So, we calculate using the formula
A = = 5586.60 dollars
Thus having $5586.60 at the account originally, you will be able to withdraw $200 every month (at the beginning of the month) during 30 monts.
Notice that you, actually, withdraw $200*30 = $6000 in total, which is MORE than the original value of the account.
It is because the earned/accumulated percentage interest provides covering the difference.
Solved.
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In this site, there is a group of lessons associated with annuity saving plans and retirement plans. They are
- Ordinary Annuity saving plans and geometric progressions
- Annuity Due saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
- Withdrawing a certain amount of money periodically from a compounded saving account (*)
- Miscellaneous problems on retirement plans
From these lessons, you can learn the subject and can see many similar solved problems.
The closest lesson to your problem is marked (*) in the list.