Question

Someone invests a constant stream of $450 per year at a continuously compounding interest rate of 5%. What is the present value of this continuous stream if it continues for 50 years? Round your answer to the nearest dollar, and do not include the dollar sign.

Answer 1

The present value of the annuity will be 8,215

Step-by-step explanation:

This will be the case of an annuity.

There is an annuity of 450 dollars, at a 5% rate for 50 years.

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

c= 450

rate = 0.05

time = 50

`450 * (1-(1+0.05)^(-50) )/(0.05) = PV\\`

PV = $8,215.1665

rounding to nearest dollar = $8,215