# NPV and annuities: how much must be saved to plan for retirement

Assume that you are planning on how much you need to save for retirement. You expect to live for 30 years in retirement and would like to spend $100,000 (in real terms) per year, while leaving a $1,000,000 bequest to the International Red Cross. You are 35 years away from retirement. How much do you need to save at the end of each year if you earn 5% real (i.e., after inflation) during your working years and 3% during your retirement years?

** Solve the problem in 2 different ways: by using a spreadsheet; by using the formulas for the present value of an annuity and for a loan payment.**

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#### Solution Preview

See the attached files.

First calculate the value of money required at the end of 35 years to sustain the expenditure after retirement.

We have two streams of cash flow. One is annuity of $100,000 every year with discount rate of 3%. One time payment of $1000,000.

Value of ...

#### Solution Summary

The solution shows all the calculations to arrive at the correct answer in two formats. How much must be saved to plan for retirement is determined.