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Your great-aunt Emma is 82 years old. Over the years, she has accumulated saving

ID: 2420656 • Letter: Y

Question

Your great-aunt Emma is 82 years old. Over the years, she has accumulated savings of $285,400. She estimates that she will live another 10 years at the most and wants to spend her savings by then. (If she lives longer than that, she figures you will be happy to take care of her.) Aunt Emma places her $285,400 into an account earning 12% annually and sets it up in such a way that she will be making 10 equal annual withdrawals (the first one occurring 1 year from now) such that her account balance will be zero at the end of 10 years. How much will she be able to withdraw each year?

Explanation / Answer

Formula for present value of an anuuity = PV= A [ (1+k)n-1/k(1+k)n]

PV = Present value of fund =285,400

A = yearly installments paid

k=interest rate=12% pa

n=periods=10years

285400=A*[1.12^10-1]/0.12*1.12^10

Or A=$ 50,511.28

Therefore she will be able to withdraw $50,511.28 each year for 10 years.