Question

An account with $300 in it has been earning 3% annual interest compounded continuously for 10 years with no deposits or withdrawals in that time. How much was in the account 4 years ago.

Answer 1

Since the annual interest is 3%, multiply the principle by 1.03 to get the amount of the principle plus the interest earned. Then, just use the new principle amount. Here's the amounts for 10 years.

1st year - $300.00 x 1.03 = $309.00
2nd year - $309.00 x 1.03 = $318.27
3rd year - $318.27 x 1.03 = $327.82
4th year - $327.82 x 1.03 = $337.65
5th year - $337.65 x 1.03 = $347.78
6th year - $347.78 x 1.03 = $358.22
7th year - $358.22 x 1.03 = $368.96
8th year - $368.96 x 1.03 = $380.03
9th year - $380.03 x 1.03 = $391.43
10th year - $391.43 x 1.03 = $403.17

Now, just count back 4 years ago, which should mean the 6th year, unless your teacher means the 7th year.