Suppose you deposit $103,000 into an account paying 7.5% simple annual interest, and that you won't touch the account until it holds $1,000,000. How long must you wait?

just solve for t in

103000(1+.075t) = 1000000

To calculate the time it will take for your initial deposit to grow to $1,000,000 with a 7.5% simple annual interest rate, we can use the formula for simple interest:

I = P * r * t

Where:
I = Interest earned
P = Principal (initial deposit)
r = Interest rate per period
t = Number of periods

In this case, we need to solve for 't', as we want to find out how long it will take for the account balance to reach $1,000,000.

Let's rearrange the formula to solve for 't':

t = I / (P * r)

Now, let's substitute the given values into the formula:

P = $103,000 (initial deposit)
r = 7.5% = 0.075 (as a decimal)
I = $1,000,000 - $103,000 (target balance - initial deposit)

I = $897,000

t = $897,000 / ($103,000 * 0.075)

t ≈ 13.84

Therefore, you would need to wait approximately 13.84 years for your account balance to reach $1,000,000 with a simple annual interest rate of 7.5%.