You would like to have 50000 plan to deposit each year an eq

You would like to have $50,000 plan to deposit each year an equal sum in the bank, which will earn 2%, compounded annually. Your first payment will be made at the end of the year. in 15 years. To accumulate this amount, you Required (a) How much must you deposit annually to accumulate this amount? (b) If you decide to make a lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 7% on this deposit.) (c) At the end of five years, you will receive $10,000 and deposit this in the bank towards your goal of $50,000 at the end of 15 years. In addition to this deposit, how much must you deposit in equal annual deposits in order to reach your goal? (Assume you can earn 7% on this deposit.)

Solution

a. PV = 0, FV = 50,000, N = 15, 1/Y = 7%

use PMT function

annual deposits = 1989.73

b. lump sum = 50,000/1.07^15 = 18,122.30

c. PV of 10,000 received = 10,000/1.07^5 = 7,129.86

PV = 7,129.86, FV = -50,000, N = 15, 1/Y = 7%

use PMT function

annual deposits = 1,206.91