Math Problem Statement

Chen is 65 years old and about to retire. She has ​$790 comma 000 saved to supplement his pension and Social Security and would like to withdraw it in equal annual dollar amounts so that nothing is left after 16 years. How much does she have to withdraw each year if she earns 5 percent on her​ money? Question content area bottom Part 1 Click on the table icon to view the PVIFA​ table: LOADING.... If Chen earns 5 percent on her​ money, the amount she will have to withdraw each year is ​$

enter your response here. ​(Round to the nearest​ cent.)

Solution

To calculate how much Chen needs to withdraw each year, we can use the Present Value of an Annuity formula. The formula is as follows:

PV=PMT×(1(1+r)nr)PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)

Where:

  • PVPV is the present value of the annuity (in this case, $790,000).
  • PMTPMT is the annual withdrawal (what we're solving for).
  • rr is the annual interest rate (5% or 0.05).
  • nn is the number of years (16 years).

We need to rearrange this formula to solve for PMTPMT (the annual withdrawal):

PMT=PV1(1+r)nrPMT = \frac{PV}{\frac{1 - (1 + r)^{-n}}{r}}

Substituting the values into the formula:

PMT=790,0001(1+0.05)160.05PMT = \frac{790,000}{\frac{1 - (1 + 0.05)^{-16}}{0.05}}

Let’s calculate this.Chen would need to withdraw approximately $72,893.23 each year if she earns 5% on her money, in order for the funds to last 16 years.

Would you like any further details or explanations on this? Here are some additional related questions you might find helpful:

  1. What happens if the interest rate changes?
  2. How would the annual withdrawal change if the time period were extended?
  3. How is the Present Value of an Annuity calculated in different financial situations?
  4. Can this formula be used to calculate monthly withdrawals instead of annual?
  5. What factors affect retirement withdrawal strategies?

Tip: Consider inflation when planning for long-term financial withdrawals to maintain your purchasing power over time.

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Math Problem Analysis

Mathematical Concepts

Finance
Annuities
Present Value

Formulas

Present Value of an Annuity formula: PV = PMT × (1 - (1 + r)^-n) / r
Rearranged formula for PMT: PMT = PV / [(1 - (1 + r)^-n) / r]

Theorems

Present Value of an Annuity

Suitable Grade Level

Grades 11-12 (Financial Math) or College Level