Question

Most scholarships are established by making a one time deposit into an account. The scholarship money is then taken from the earned interest on the account at the end of each investment year. How much money should you deposit into an account earning an annual interest rate of 5.968% compounded monthly to establish an annual scholarship worth $600.00? I need to make the $600 in interest each year, I just can't seem to get the right answer

Answer 1

You deposit P dollars into the account at time 0. After a year, you want to have earned $600 in interest, which is compounded monthly at the given rate.
The (non-continuous) compound interest formula is
\[A=P\left(1+\frac{r}{n}\right)^{nt}\]
where A is the amount of money in the account after time t,
P is the initial amount deposited,
r is the given interest rate, and
n is the number of times interest is compounded annually.

You want 600 at the end of the year, so A = 600 + P. (Do you see why?)

So, the equation set-up is
\[600 + P = P\left(1+\frac{.05968}{12}\right)^{12\cdot1},\]
and you're left to solve for P.

Answer 2

Doesn't that cancel out the P though? When you divide 600 by what the (1+.05968 etc.) it gives me 565.325 +P =P, so you'd subtract the P, and then...

Answer 3

I'll write the coefficient of P as x, so you have
600 + P = xP

You do not divide right away. That won't help in solving for x. Instead, do this:
600 + P - xP = 0
P - xP = -600
P (1 - x) = -600
P = -600/(1 - x)

Answer 4

okay, I understand where you're going with this, however the numbers I keep getting aren't right, do you know what the answer is? Or at least if I'm using the right numbers? for x I'm putting in (1+.(05968/12)^12) which is coming up as 1.06134

Answer 5

Nevermind it came up right this time! Thank you SO Much! I've been working on this for hours!