Maximizing Consumption in Retirement: A Two-Period Financial Planning Problem

Maximizing Retirement Consumption: A Two-Period Model

This example analyzes how Lara Beal can maximize her consumption in retirement given her current financial situation and available investment options.

The Problem: Lara has $8,000 in cash during her youth and wants to maximize her consumption in old age. She has two options:

1. Invest in a Project: The project costs $5,000 today and pays off $6,000 in her old age.2. Invest in a Bank Account: The bank offers a 15% interest rate per period (youth to old age).

Solution:

To make the best decision, we need to compare the future value of each option:

Option 1: Investing in the Project

• Calculate the Present Value (PV) of the project's payoff: This tells us how much the future $6,000 payoff is worth today considering the time value of money.

  PV = Future Payoff / (1 + Interest Rate)^Number of periods PV = $6,000 / (1 + 0.15)^1 PV = $5,217.39

Option 2: Depositing in the Bank

• Calculate the Future Value (FV) of the bank deposit: This tells us how much money Lara will have in her old age if she deposits her $8,000 in the bank.

  FV = Initial Amount * (1 + Interest Rate)^Number of periods FV = $8,000 * (1 + 0.15)^1 FV = $9,200

Comparison:

• Project Investment: Provides $5,217.39 in old age.* Bank Deposit: Provides $9,200 in old age.

Conclusion:

Lara can consume the most in her old age by depositing the entire $8,000 in the bank. This strategy yields the highest future value, allowing her to consume up to $9,200 in her old age.