You have purchased a deffered annuity. In this case you pay $10,000 today and th

Question

You have purchased a deffered annuity. In this case you pay $10,000 today and the insurnace company will begin to pay you yearly  payments in 15 years. Your $10,000 grows at 6% per year compounded annually for 15 years. At he end of year 15 your defrred annuity begins to make payments such that the amount in your annuity account pays you a constant payment for 30 years or untill you pass-away. The interst rate that the insurance compnay uses to calcuate your payments is 4% per year. What are your yearly annuity payments?

Explanation / Answer

Value accumulated at end of 15 years = A * (1 + i)^n

= 10000 * (1 + .06)^15

= 23965.58

Annuity payments:

PV = A * (1-(1+i)^-n)/i

23965.58 = A * (1-(1+.04)^-30)/.04

A = 1385.93

yearly annuity payments = 1385.93

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