Question

​) You would like to have ​$33 comma 00033,000 in 1515 years. To accumulate this amount you plan to deposit each year an equal sum in the​ bank, which will earn 99 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 99 percent on this​ deposit.) c. At the end of 66 years you will receive ​$12 comma 00012,000 and deposit this in the bank toward your goal of ​$33 comma 00033,000 at the end of 1515 years. In addition to this​ deposit, how much must you deposit in equal annual deposits to reach your​ goal? (Again assume you can earn 99 percent on this​ deposit.)

Answer 1

a)Future value = Annual deposit * FVA9%,15

     33000 = Annual deposit * 29.36092

     Annual deposit = 33000/ 29.36092

                         = $ 1123.94 per year

**Find future value annuity factor from future value annuity table at 9% for 15 years

b)

Future value =Amount to deposit today *FVF 9%,15

33000 = Amount to deposit today * 3.64248

Amount to deposit today = 33000 / 3.64248

                             = $ 9059.76

***Find future value factor from future value table at 9 % for 15 years

c)

Future value of amount received at end of year 6 (15years -6 years =9)	FVF9%,9*Amount	2.17189*12000 26062.68
Future value of annuity	FVA9%,15*annual deposit	Balancing figure [33000-26062.68] 6937.32
Future value at end of 15 years		33000

Future value of annuity = FVA9%,15* annual deposit

6937.32 = 29.36092 *Annual deposit

Annual deposit = 6937.32 /29.36092

                     = $ 236.28