Question

Franklin deposits $3500 in an account that earns 3.5% interest compounded annually.

What function equation represents the balance of the account after t years?

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Answer 1

May I help?

Answer 2

Of course.

Answer 3

I will simplify it it you as much as I can!!!!

We are dealing with Compound or Complex interest rate, which has the following characteristic:

at the beginning (t=0): amount of money is \(3500\)

at the end of the 1st year(t=1), it counts a rate of: \(3500*0.035^1=122.5\) in addition to the original amount \(3500\), so the total money at the end of the first year: \(3500+122.5=3622.5\)

for the 2nd year (t=2), the interest rate would be calculated on the amount of money at the end of the first year (3622.5), so the rate would be: \(3622.5*0.035=126.7875\) and then it would be added to \(3622.5\), so the money at the end of the 2nd year is \(3622.5+126.7875=3749.28 \)

Answer 4

So D?

Answer 5

\[f(t)=[3500]+[3500+3500*0.035]\\~~~~~~~~~~+[(3500+3500*0.035)+(3500+3500*0.035)*0.035]+...\\=3500[1+0.035]^t\]

Answer 6

D is the correct choice if we just want to calculate the money gained from the interest!

But in case we want to calculate the balance of the account after t year elapsed....it would be \((1+0.035)^t\)

Answer 7

Thank you.

Answer 8

Not at all!
Did you get the idea?