Question

In: Finance

) You would like to have $33 comma 00033,000 in 1515 years. To accumulate this amount...

) 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.)

Expert Solution

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

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