Application to Economics

[Marierose]

A bank account earns 10% interest compounded continuously. At what (constant, continuous) rate must a parent deposit money into such an account in order to save $100,000 in 10 yrs? How much for a lump sum

I tried using the formula B=Pe^rt to get the lump sum and i solved for P to get P=Be^-rt. Then i substituted 100,000 for B and i got 36787.94.

Now i am confused as to what i need to do for the first part. (What constant,continuous) rate must a parent deposit to get 100,000 in 10 years.

Please help!!!

 

[galactus]

You have the rate, 10%. Don't you mean what amount should they initially invest to have 100,000 in 10 years?.

\(\displaystyle \L\\A=A_{0}e^{rt}\)

\(\displaystyle \L\\100,000=A_{0}e^{(0.10)(10)}\)

Solve for \(\displaystyle A_{0}\)

I get, as you, $36,788.

Your other question, what rate?, makes no sense. You are given the rate.

 

[Marierose]

Thanks so

100,000=P(e^1)
100,000/e^1=P
P=36,787.94

So does this means that both questions are asking the same thing in different way?[/u]