Dr. Finan FM/2 - Problem 4.9(Simple interest rate)

[StatGuy3]

Problem 4.9
Suppose that the accumulation function for an account is a(t) = 1 + 3it

At time 0, you invest $100 in this account.

If the value in the account at time 10 is $420, what is i?

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The solutions manual says 10.66%, however, I got 14% after doing it a couple of more times.

PV = 100
FV = 420
a(0) = 1
a(10) = 1 + 30i

420 = 100 * (1 + 30i - 1 / 1 )

i = 14% from here. However, while I'm sure it's 14%, I'm not 100% sure. If it's 10.66% as the solutions say, could someone point this out? Thanks!

[BeanCounter]

The equation you set up is wrong.

Let me rearrange your equation:
420/100 = (1 + 30i -1 / 1 )

LHS = the final value / initial value
RHS = (the final value - initial value / initial value)
I think you may want your RHS to be (1 + 30i -1 ) / 1 which is (the final value - initial value ) / initial value

Anyway, LHS <> RHS.

Now, I think you know what's wrong with your equation.

[Happychick90]

I didn't understand BeanCounter's explanation, so I set it up the way I learned it.
100a(10) = 420
100[1+3i(10)] = 420