Question

Find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.)
Achieve $225,500 at 8.55% compounded continuously for 8 years, 145 days.

Answer 1

Task. Find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.) Achieve $225,500 at 8.55% compounded continuously for 8 years, 145 days.

Solution. Recall that continuous compound interest formula has thefollowign form:

$A=Pe^{rt},$

where

- $P$ is the principal amount (initial investment),

- $r$ is the annual interest rate (as a decimal),

- $t$ is the number of years,

- $A$ is the amount after time t.

Hence

$P=Ae^{-rt}.$

We have that

$A=$ $225,500,$

$r=$ $8.55\%=0.0855.$

Assume that the year has 365 days, then

$t=8+\frac{145}{365}\approx 8.39726.$

Substituting into the formula we get

$P=Ae^{-rt}=225500*e^{-0.0855*8.39726}=225500*e^{-0.71797}\approx 225500*0.48774\approx 109985.37.$

Answer. $109,985.37