Annuities Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
You want to receive \1{,}000permonthfor per month for 20yearsfromaretirementaccountearning years from a retirement account earning 5\%$ annual interest compounded monthly. How much must be in the account at the start of retirement?

Solution

  1. 1
    This is the present value of an ordinary annuity: PV=Pโ‹…1โˆ’(1+r)โˆ’nrPV = P \cdot \frac{1 - (1+r)^{-n}}{r}. Here r=0.0512โ‰ˆ0.004167r = \frac{0.05}{12} \approx 0.004167, n=240n = 240, P=1000P = 1000.
  2. 2
    PV = 1000 \cdot \frac{1 - (1.004167)^{-240}}{0.004167} = 1000 \cdot \frac{1 - 0.3693}{0.004167} = 1000 \cdot \frac{0.6307}{0.004167} \approx \151{,}369$.

Answer

โ‰ˆ$151,369\approx \$151{,}369
The present value of an annuity tells you how much a series of future payments is worth today. You need \151{,}369tofund to fund \1,0001{,}000 monthly payments for 20 years, even though the total payments are \240{,}000$, because the remaining balance continues earning interest.

About Annuities

A series of equal payments made at regular intervals over a fixed period of time. The future value and present value formulas calculate the total worth of these payment streams.

Learn more about Annuities โ†’

More Annuities Examples

Example 1 easy

You deposit [formula]200[formula]6%[formula]1$ year?

Example 2 medium

What monthly payment is needed to accumulate [formula]50{,}000[formula]10[formula]4.8%$ annual inter

Example 4 hard

Compare an ordinary annuity and an annuity due, both with [formula]500[formula]6%[formula]5$ years.

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