(Comprehensive problem) You would like to have $51,000 in 13 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 10 percent interest compounded annually. Your first payment will be made at the end of the year. a. How much must you deposit annually to accumulate this amount? b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 10 percent on this deposit.) c. At the end of five years, you will receive $10,000 and deposit this in the bank toward your goal of $51,000 at the end of year 13. In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? (Again, assume you can earn 10 percent on your deposits.) a. How much must you deposit annually to accumulate this amount? $ (Round to the nearest cent.) b. If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should the lump-sum deposit be? $ (Round to the nearest cent.) c. If you deposit $10,000 received at the end of five years in the bank, what will the amount grow to by the end of year 13? $ (Round to the nearest cent.) In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? $ (Round to the nearest cent.)