how much money invested at 5% compounded continuously for 3 years will result in $820?

Question

how  much money invested at 5% compounded continuously for 3 years will result in $820?

atianaaaa · Answer

i know the answer just need the work

anonymous · Answer

$$amount=principal(1+\frac{ rate }{ hundred  } )^{time}$$

atianaaaa · Answer

i got that part too so how do we work it ? @surjithayer

ltrout · Answer

Well you know amount has to equal 820. Time is 3 years. 5% interest.

So 
820 = principal(1+5/100)^3.

ltrout · Answer

Now just solve for principal

atianaaaa · Answer

how would i do that

ltrout · Answer

Well you would want to get principal on one side. So
$$principal = \frac{ (1+\frac { (5) }{ (100)})^{3} }{ 820 }$$

And then just solve the equation.

atianaaaa · Answer

and the answer would 705.78?

ltrout · Answer

Let me do the math real quick. One way to check is to just do y=705.78(1.05)^3 and see if that comes out to be 820.

atianaaaa · Answer

awe no i got 8.17

atianaaaa · Answer

no what would be the answer now im confused

ltrout · Answer

Oops. Sorry should be 820 in the numerator and the other portion in the denominator. You should come out with an answer of 708.35 (rounded to the hundredth). You can check this answer by doing y = 708.35(1.05)^3 which comes out to be 820.

atianaaaa · Answer

wait what was that first part ?

ltrout · Answer

So how I put principal = (1+(5/100))^3/820, it should be principal = 820/(1+(5/100))^3. Which would leave you with an answer of 708.35. Then to check that you would do y = 708.35(1.05)^3. Which would come out to be 820.

atianaaaa · Answer

oh okay thank you can you help me with one more word problem ?