Kiran plans to save \$200 per year. Bank A would pay 6% interest, and Bank B would pay 4% interest (both compounded annually). How many years will it take to save \$10,000 if he uses Bank A? Bank B?

Find the sum of the first 20 terms of each sequence:

1. \( 1, \frac23, \frac49,\frac8{27},\frac{16}{81},\dots\)

2. \( 3, \frac63,\frac{12}9,\frac{24}{27},\frac{48}{81},\cdots\)

3. \( 4,2,1,\frac12,\frac14,\cdots\)

Diego wonders how much money he could save over 25 years if he puts $150 a year into an account with 4% interest compounded annually (once per year). He calculates the following, but thinks he must have something wrong, since he ended up with a very small amount of money:

\( \displaystyle \text{total amount} =150 \, \frac{1-0.04^{25}}{0.96} = 156.25\)

What did Diego forget in his calculation? How much should his total amount be? Explain or show your reasoning.