SOLUTION: Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period. $20,000; quarterly pa

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Question 1185955: Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period.
$20,000; quarterly payments for 17 years; interest rate 5%
the payment should be? $
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
the future value is 20,000.
the number of quarterly payments = 17 years * 4 = 68 quarters.
the interest rate per quarter = 5% / 4 = 1.25% per quarter.

the calculator at https://arachnoid.com/finance/index.html can get the answer for you.

here are your inputs.

here is your output.

your inputs are everything except pmt.
your output is pmt.

the quarter by quarter remaining balance, payment, interest part of payment, equity part of payment, are shown below for the first few quarters and the last few quarters.

the procedure for each time period is shown by the following example:

the payment and the interest in time period 62 is added to the remaining balance in time period 61 to get the remaining balance in time period 62.

that would be 17079.43 + 188.34 + 213.49 = 17481.26.

the difference in this value plus what is shown in the spreadsheet (17481.47) has to do with rounding.
the numbers shown in the spreadsheet are rounded.
the actual calculations are done with unrounded numbers not shown in the display.

for example:
the actual remaining balance in time period 61 is equal to 17079.42849.
the actual payment amount is 188.3448429.
the actual interest is 17079.42849 * .04/5 = 213.4928561.
17079.42849 + 213.4928561 + 188.3448429 = 17481.26619.
round that to 2 decimal digits and it equals 17481.27 as shown in the excel results for remaining balance in time period 62.

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.
Find the payment that should be used for the annuity due whose future value is given.
Assume that the compounding period is the same as the payment period.
$20,000; quarterly payments for 17 years; interest rate 5% the payment should be?
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            What @Theo calculated for you, was the Ordinary Annuity saving plan, when the regular deposits are made at the END of each quarter.
            The given problem asks about the Annuity Due saving plan, when the regular deposits are made AT THE BEGINNING of each quarter.

            So, @Theo's calculations are not appropriate for this problem.

            THEREFORE, I came to bring you a correct solution.

It is a classic Annuity Due saving plan. The general formula is FV = , (1) where FV is the future value of the account; P is your quarterly payment (deposit), which is made at the beginning of each quarter; r is the effective quarterly percentage yield presented as a decimal; n is the number of deposits (= the number of years multiplied by 4, in this case). Under the given conditions, FV = 20000; r = 0.05/4; n = 17*4 = 68. So, according to the formula (1), the quarterly payment should be P = = $186.02. ANSWER Note that you deposit only 17*4*$186.02 = $12,649.36. The rest is what the account earns/accumulates in 17 years.

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On Ordinary Annuity and Annuity Due saving plans, see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
    - 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.