Mathematics: Me with these 2 multiple choice questions?

Me with these 2 multiple choice questions? - id21045232, peytondavis2424

vhs35

29.09.2022

Step-by-step explanation:

Consider the function of the rate of flow of money in dollar per year is

$f(t)= 400e^{0.03t}$

The objective is to find the present value of this income over 10 years period an assume an annual interest rate of 8% compounded continuously.

Given that,

$f(t)= 400e^{0.03t}$

r = 0.08, t = 10

if f(t) is the rate of continuously money flow at an interest rate r to T year,

the present value is,

$P= \int\limits^T_0 {f}(t)e^{-rt} \, dt$

Now input the values to get

$p=\int\limits^{10}_0 400e^{0.03t}*e^{-0.08t} dt$

$=400\int\limits^{10}_0 e^{0.03t}*^{-0.08t} dt$

$= 400\int\limits^{10}_0 e^{-0.05t} dt$

$=400(-\frac{e^{-0.05t}}{0.05} )|_0^1^0$

$=-\frac{400}{0.05} (e^{-0.05*10}-e^{-0.05*0})\\\\=-\frac{400}{0.05} (e^{-0.5}-e^{*0})\\\\=3147.75$

Therefore, the present value is $3147.75

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