Question

How long must the $4800 be in the bank at 7% compounded annually to become $9442.33?
Thanks!! ;)

Answer 1

9442.33 <= 4800(1.07)^y

ln (9442.33/4800) <= ln (1.07)^y

ln (9442.33/4800) <= (y)(ln 1.07)

(ln 9442.33/4800)/(ln 1.07) <= y

10 <= y

Answer 2

As a check, you'll see that:

9442.33 = 4800(1.07)^10 (rounded)

Answer 3

Thank you, Can you explain me why it is 1.07?

Answer 4

First, you're welcome.

To make things easiest, just look at one dollar, and you can multiply it by 4800 later. So, for one dollar:

Now, 1.07 is from 1 + 0.07 which is written out this way because after one year you have your principal plus your interest. One dollar and 7 cents which is (1)(1 + 0.07)

At the end of 2 years, you have (1.07)(1 + 0.07) or (1.07)(1.07) or 1.07^2

At the end of 3 years, you have (1.07)^2(1 + 0.07) or (1.07)^2(1.07) or 1.07^3

And so on.

Answer 5

Ohh waooo!! Good explanation, Thanks so much!!! ;)

Answer 6

Wonderful when the light bulb goes on! That's when we make progress with math! It's fun!

Answer 7

Yes that's true...!! lol!