Lesson Accumulate money using ordinary annuity; then spend money via sinking fund

Accumulate money using ordinary annuity; then spend money via sinking fund

Problem 1

Let' solve this problem into two parts:


        Part 1: Calculate the Accumulated Value of Grandma's Deposits


1. Monthly Deposit:   $1300
2. Number of Deposits:   23
3. Interest Rate:         9.3% compounded monthly (effective rate r = 0.093/12 per month)


Use the future value of an ordinary annuity formula:

    FV = ,    (1)

where

  FV = Future Value
  P = Periodic Payment ($1300)
  r = Interest Rate per Period (0.093/12)
  n = Number of Periods (23)

    FV =     (2)


Use MS Excel software in your computer.
It is commonly considered as an appropriate tool for such calculations, 
since it provides the necessary precision.
Copy and paste this formula into a MS Excel, and get the value of $32,592.78.

Do not make intermediate rounding, since intermediate rounding are PROHIBITED 
in such calculation: they influence to the final result and lead to wrong answer.


        Part 2: Calculate the Monthly Withdrawal Amount


1. Accumulated Value (Present Value for Withdrawals):   $32592.78
2. Number of Withdrawals:                                   58
3. Interest Rate:   9.3% monthly (effective compounding rate r = 0.093/12 per month)


Use the present value of an annuity due formula since withdrawals are at the beginning of each month:

    PV = ,    (3)

where:

  PV = Present Value ($32592.78)
  M = Monthly Withdrawal Amount
  r = Interest Rate per Period (0.093/12)
  n = Number of Periods (58)

Rearrange the formula (3) to solve for M:

    M = ,   (4)


    M = .    (5)


Again, use MS Excel software in you computer.
It is commonly considered as an appropriate tool for such calculations, 
since it provides the necessary precision.
I copied and pasted this formula into a MS Excel, and I got the value of $694.43.

Do not make intermediate rounding, since intermediate rounding are PROHIBITED 
in such calculation: they influence to the final result and lead to wrong answer.


Answer.  You will be able to withdraw approximately $694.43 at the beginning of each month.