# Thread: differential word problem

1. ## differential word problem

Suppose that we want a certain endowment to pay 50,000 dollars in cash ten years from now. The endowment will be set up today with 5,000 dollars principal and locked in at a fixed interest rate. What interest rate (compounded continuously) is needed to guarantee the desired payoff?

I know that Amount = P(1+(r/100n)^(10n) but I can't figure out the rate.

2. Originally Posted by keemariee
Suppose that we want a certain endowment to pay 50,000 dollars in cash ten years from now. The endowment will be set up today with 5,000 dollars principal and locked in at a fixed interest rate. What interest rate (compounded continuously) is needed to guarantee the desired payoff?

I know that Amount = P(1+(r/100n)^(10n) but I can't figure out the rate.
If you are saying find the slope for

$\displaystyle y=P\bigg(1+\bigg(\frac{r}{100n}\bigg)^{10n}\bigg)$?

then the slope in respect to which letter??

3. Originally Posted by keemariee
Suppose that we want a certain endowment to pay 50,000 dollars in cash ten years from now. The endowment will be set up today with 5,000 dollars principal and locked in at a fixed interest rate. What interest rate (compounded continuously) is needed to guarantee the desired payoff?

I know that Amount = P(1+(r/100n)^(10n) but I can't figure out the rate.
I don't normally do financial mathematics (unless I'm charging like a wounded bull some company or another) but I'll make an exception here.

You have the wrong formula if the principle is compounded continuously. The correct formula is

$\displaystyle A = A_0 e^{rt}$

where t is the number of years, A is the amount after time t, $\displaystyle A_0$ is the initial invetsment and r is the annual interest rate.

Substitute the given values for t, A and $\displaystyle A_0$ and solve for r.