another compounding interest question - continuous?

Question

I think I almost have this one figured out. I am just trying to isolate Po from the equation.

How much money must you put into an investment today to yeld a lump sum of $50,000 in 25 years time, if interest is compounded continuously at an apr of 5.25%?

P(t)=Poe^(i*t)

where t=25 years, i=.0525, and P(25)=$50,000.

I have:

50,000=Poe^(.0525*25)

0=Poe^(1.3125)-50000

Now I'm stuck. Do I divide by Po to get it on the right side of the equation? Please help!!!

Thanks in advance.

Answer 1

I = Pe^(rt)

50000 = Pe^(25 * .0525)
50000 = Pe^(1.3125)
P = 50000/(e^(1.3125))
P = $13,457.32

Answer 2

You are missing the forest because of the trees
First, don't play with the 50K until you must. As in the last question, isolate the exponential to get
P(t)/Po = exp (i T)
P(25)/Po = exp(1.3125) = 4 (appx).
NOW, put it 50K for Po.

Answer 3

Po is your original investment.

(Po)(1.0525^25) = 50000

Po = 50000/(1.0525^25) = $13912.89

Answer 4

I do believe so but i haven't takin a math class that level for year....(college is easier than that)