Question

Find the PV of a 15-year annuity with continuous payments at the rate of $250 a year at a force of interest δ = 3.9%. Possible Answers

A 2839
B 2923
C 3853
D 3225
E 4096

Answer 1

The present value of a 15-year annuity with continuous payments is $2839 (option A).

Step-by-step explanation:

To find the present value (PV) of a 15-year annuity with continuous payments at a rate of $250 a year and a force of interest of 3.9%, we can use the formula: PV = Payment * (1 - e^(-δ*t)) / δ

{ where PV is the present value, Payment is the payment amount, δ is the force of interest, and t is the number of years.}

In this case, PV = $250 * (1 - e^(-0.039*15)) / 0.039

= $2838.75.

Therefore, the correct answer is A). 2839.