Question

(Complex present value) You would like to have $30,000 in 16 years. To accumulate this amount you plan to deposit each year an equal sum in the bank, which will earn 7 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 7 percent on this deposit.) c. At the end of 5 years you will receive $10,000 and deposit this in the bank toward your goal of $30,000 at the end of 16 years. In addition to this deposit, how much must you deposit in equal annual deposits to reach your goal? (Again assume you can earn 7 percent on this deposit.) a. How much must you deposit annually to accumulate $30,000 in 16 years? $ 1075.73 (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 this lump-sum deposit be? (Assume you can earn 7 percent on this deposit.) $ 10162.04 (Round to the nearest cent.) c. At the end of 5 years you will receive $10,000 and deposit this in the bank toward your goal of $30,000 at the end of 16 years. In addition to this deposit, how much must you deposit in equal annual deposits to reach your goal? (Again assume you can earn 7 percent on this deposit.) $ (Round to the nearest cent.)

Answer 1

a)

FV = 30,000

nper = 16 years

rate = 7%

Annual deposit amount(PMT) =
=pmt(7%,16,,30000 PMT(rate, nper, pv, [fv], [type])
= $ 1075.73

b)

Large lumpsum amount today(PV)=
=pv(7%, 16, 30000 PV(rate, nper, pmt, [fv], [type])
= $ 10,162.04

c)

Number of years = 11 years

Rate = 7%

Initial Deposit Amount = $ 10,000

FV of deposit amount = 10,000*(1+7%)^11 = $ 21,048.52

Difference in FV of deposit amount and the required amount at the end of 16 years = (30,000 - 21,048.52) = $ 8,951.48

Equal deposit amount to reach this figure = (where B355 = $ 8951.48)

=pmt(7%,11,,B355 PMT(rate, nper, pv, [fv], [type])

= $ 567.14