Question

You would like to have $48,000 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 6 years you will receive $10,000 and deposit this in the bank toward your goal of $48,000 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.)

Answer 1

Answer to point A

PV = FV / {[1/(1+r)]ⁿ -1 } / r

FV = Future Value =$48000

PV = Present Value = ?

r = rate of Return = 7%

n = No of years = 16 years

PV  = FV / {[1/(1+r)]ⁿ -1 } / r

PV = $48000 / {[1/(1+.07)]¹⁶ -1 } / .07

PV = $48000/ 9.4466

PV = $5081 = amount to be deposited annually to get 48000 after 16 years

Answer to Point B :

PV = FV / (1+r)ⁿ

FV = Future Value =$48000

PV = Present Value = ?

r = rate of Return = 7%

n = No of years = 16 years

PV = $48000 / (1+.07)¹⁶

PV = $48000/2.2522

PV = $21312.49 = Amount to be deposited today to get $48000 after 16 years

Answer to Point C:

FV= PV *(1+r)ⁿ

FV = Future Value =?

PV = Present Value = 10000

r = rate of Return = 7%

n = No of years = 10 years

FV= $10000 * (1+.07)¹⁶

FV = $10000 * 2.2522

FV=$22522

Remaining Future value = $48000-22522

Remaining Future value = $25478

PV = FV / {[1/(1+r)]ⁿ -1 } / r

PV = $25478 / {[1/(1+.07)]¹⁶ -1 } / .07

PV = $25478/ 9.4466

PV = $2697 = Annually to be paid from year1 to year 16 and $10000 in year 6 to get $48000 at the end of year 16.