Sarah currently has $62,410 in her retirement account, and her goal is to have at least $100,000 in the account. The account earns 6.9% interest on the balance, compounded annually. Sarah does not make any additional withdrawals or deposits. What is the fewest number of years it would take Sarah to reach her goal?

We need to make an equation to solve how much money she would have in x years.
[tex]62,410*1.069^{x} =y[/tex]
We need to find X when y is 100,000.
62,410×1.069^x=100,000
We should divide both sides by 62,410.
1.069^x=1.60230732
With this, I would find what 1.069² is to find if it's close.
1.069²=1.142761
Now, it to the 10th.
1.069^10=1.949
1.069^5=1.396
1.069^8=1.70538
1.069^7=1.595
The fewest number of years it would take Sarah to reach her goal is 7.06563254.
62,410×1.069^7.06563254=99,999.9998707