Determine the difference between the present value of a $51,000 twenty-year annuity earning 6% interest compounded annually versus a $51,000 twenty-year growing annuity earning 6% interest
Compounded annually and having a 3% annuity growth rate.

Question

Quizplus · Accepted Answer

The present value of the regular annuity can be calculated using the formula PV = Pmt * [1 - (1+r)^-n] / r, where Pmt is the payment, r is the interest rate, and n is the number of periods. Plugging in the given values, we get:

PV = 51,000 * [1 - (1+0.06)^-20] / 0.06
PV = $600,882.34

The present value of the growing annuity can be calculated using the formula PV = Pmt / (r-g) * [1 - ((1+g)/(1+r))^n], where g is the growth rate. Plugging in the given values, we get:

PV = 51,000 / (0.06-0.03) * [1 - ((1+0.03)/(1+0.06))^20]
PV = $758,554.52

The difference between the two values is $758,554.52 - $600,882.34 = $157,672.18

Therefore, the best choice is C) $157,672.18

Determine the Difference Between the Present Value of a $51,000