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dybincka [34]
3 years ago
8

Exit

Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
8 0

Answer:

its (B) 80

Step-by-step explanation:

i got it right

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Help please
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If Triangle ABC is similar to triangle DEF, then ∠A is congruent to ∠D, ∠B is congruent to ∠E, and ∠C is congruent to ∠F.

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The function in Exercise represents the rate of flow of money in dollars per year. Assume a 10-year period at 8% compounded cont
anzhelika [568]

Answer:

a) The present value is 688.64 $

b) The accumulated amount is 1532.60 $

Step-by-step explanation:

<u>a)</u><u> The preset value equation is given by this formula:</u>

P=\int^{T}_{0}f(t)e^{-rt}dt

where:

  • T is the period in years (T = 10 years)
  • r is the annual interest rate (r=0.08)

So we have:

P=\int^{T}_{0}(0.01t+100)e^{-rt}dt

Now we just need to solve this integral.

P=\int^{T}_{0}0.01te^{-rt}dt+\int^{T}_{0}100e^{-rt}dt

P=e^{-0.08t}(-1.56-0.13t)|^{10}_{0}+1250e^{-0.08t}|^{10}_{0}

P=0.30+688.34=688.64 $

The present value is 688.64 $

<u>b)</u><u> The accumulated amount of money flow formula is:</u>

A=e^{r\tau}\int^{T}_{0}f(t)e^{-rt}dt

We have the same equation but whit a term that depends of τ, in our case it is 10.

So we have:

A=e^{r\tau}\int^{T}_{0}(0.01t+100)e^{-rt}dt=e^{0.08\cdot 10}P

A=e^{0.08\cdot 10}688.64=1532.60 $

The accumulated amount is 1532.60 $

Have a nice day!

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