Question

Suppose you deposit $5,000 in a savings account that earns 3% annual interest. If you make no other withdrawals or deposits, how many years will it take the account balance to reach at least $6,000?

10 years
6 years
7 years
4 years

Answer 1

5000(1.03)^y >= 6000

Can you do logs?

Answer 2

no :/

Answer 3

ok,

(1.03)^y >= 6/5 -> ln (1.03)^y >= ln 6/5

(y)(ln 1.03) >= ln 6/5 -> y >= (ln 6/5) / ln 1.03

y >= 6.168

So, with whole years, you need to get to 7 years.

Answer 4

To verify this, you can take the equation in my first post with y=6 and with y=7. With y=6, you will see that you are short, but with y=7, you go over 6000.

Answer 5

All good now?

Answer 6

thanks!