A) An individual saves \( \$ 1000 \) in a bank account at the beginning of each year. The bank offers a return of \( 8 \% \) compounded annually. (1) Determine the amount saved after 10 years. (2) After how many years does the amount saved first exceed \( \$ 20000 \) ? B) The value of a good rises by \( 13 \% \) in a year. If it was worth \( \$ 6.5 \) million at the beginning of the year, find its value at the end of the year.

Step 1 ：\( A = P \cdot \frac{(1 + r)^{nt} - 1}{r} \)

Step 2 ：\( A = 1000 \cdot \frac{(1 + 0.08)^{10} - 1}{0.08} \)

Step 3 ：\( A = 1000 \cdot \frac{2.1589 - 1}{0.08} \)

Step 4 ：\( A = 1000 \cdot 14.486 \)

Step 5 ：\( A = 14486.00 \)

Step 6 ：\( n = \frac{\log(1 + \frac{A \cdot r}{P})}{\log(1 + r)} \)

Step 7 ：\( n = \frac{\log(1 + \frac{20000 \cdot 0.08}{1000})}{\log(1 + 0.08)} \)

Step 8 ：\( n = \frac{\log(1 + 1.6)}{\log(1.08)} \)

Step 9 ：\( n = \frac{\log(2.6)}{\log(1.08)} \)

Step 10 ：\( n = 14.0781 \)

Step 11 ：\( V = P \cdot (1 + r)^t \)

Step 12 ：\( V = 6.5 \cdot (1 + 0.13)^1 \)

Step 13 ：\( V = 6.5 \cdot 1.13 \)

Step 14 ：\( V = 7.345 \)