Your mother retired today and has the option of purchasing an annuity. If she ex
ID: 2650349 • Letter: Y
Question
Your mother retired today and has the option of purchasing an annuity. If she exchanges $38,000 of her savings today for a 8%, 19 yr annuity, what will her annual cash flow be? Note: You are exchanging cash today for a series of cash flows. This is an annuity problem, where the value of the annuity is defined at the START of all cash flows, so use the PV of an annuity equation. You already know what the annuity is worth today (PVa), the number of payments (t), as well as the discount rate (r). You only need to calculate C, the size of the cash flow C(1-(1+r)-n)/r)
answer selection
3,676.61
2,000
3,956.85
4,245.76
Explanation / Answer
Formula to calculate amount of Annuity: C (1 - (1+R) -N) / R)
C = Present Value = 38,000
R = Rate of Interest = 8%
N = Number of Years = 19
If we put value in the formula: 38,000 (1 - (1 + 0.08) -19 ) / 0.08)
Annuity = 3,956.85
So, the correct answer is $3,956.85
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