Question

Suppose a pension company sells a different kind of annuity. If you buy this annuity, then you will get $45,000 per year for 30 years. But the first cash-flow will be made 5 years from your purchase of the annuity. The interest and discount rates are 2%/year, compounded annually. What is the present value of this annuity? (Hint: You need to take 2 steps to find the present value of this different kind of annuity. Compute the present value of this annuity at 4 years from now, not as of today, using the standard annuity formula. Then, compute its present value (as of today) again using the present formula for a single cash-flow treating the answer from the first step as one hypothetical single cashflow in 4 years.) 1. $931,088.84 2. $933,088.84 3. $935,088.84 4. $937,088.84 5. $939,088.84

Answer 1

The answer is: "1. $931,088.84".

Step-by-step explanation:

The present value of this annuity at 4 years from now using the standard annuity formula, is calculated as below:

(45,000/2%) * [1 - 1.02^(-30)] = $1,007,840.5;

The present value of this annuity as of today is calculated by discounting the present value of this annuity at 4 years from now at the required return 2% by 4 periods, with calculations as shown below:

$1,007,840.5 / 1.02 ^4 = $931,088.84.

So, the present value of this annuity is $931,088.84; and the answer is "1. $931,088.84".