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# Finding annuity

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You plan to take a long trip through Europe, leaving in 5 years. You're plan is to save money for the next five years, leave at the end of the fifth year, and then survive on your savings for 3 years. You estimate you can survive in Europe on \$10,000 a year. You estimate that your investment account will earn 8% forever. Your account has \$1000 in it today (t=0).

Take me through the steps (no more than 4 steps) of how you would calculate the amount you must deposit in years t=1-5, assuming the deposits will be of equal amounts. [Either show me the formulas associated with each step, or show me the Excel functions with the appropriate arguments reported as well]. Be clear: write things like "add this amount to the amount calculated in Step 1." You may also use notation like: =-PV(10%,15,Step 1 value).

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Step 1

Calculate the Present value of \$10,000 a year for 3 years (year 6,7,8) at the end of 5 years

\$25,771 calculated using Excel function PV(8%,3,-10000)

Step 2

Future value of \$1000 that we have now at the end of 5 years

\$1,469 calculated using Excel function FV(8%, 5,0,-1000)

This value is subtracted from the amount calculated in Step 1

\$24,302 =25771-1469

Step 3
The future value of equal payments for 5 years must equal the amount calculated in Step 2

\$4,142 calculated using Excel function PMT(8%,5,,24302)

Answer: the amount to be deposited in years t=1-5 is equal to= \$4,142

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