Question

a) on your sister’s 10th birthday, your parents want to invest a certain amount to enable her to withdraw R25 000 every six months from her 18th to her 24th birthday (both birthdays included). Calculate the sum they will have to invest if compounded interest is estimated at 12% per annum, compounded biannually.

b) What is the present value of a perpetuity that pays R4 800 per year if the first payment does not begin until four years later and if 12% per annum is the relevant discount rate?

c) If you want to withdraw R1 000 annually for the next nine years, and R1 500 annually in the three years thereafter with all payments occurring at the end of each year, determine the amount you should initially invest to fund your withdrawals given a rate of return of 7% per annum. Round your answer to the nearest Rand

Answer 1

Solution:-

a)For calculating above first required to find out the amount shall be required in his account at the age of 18.For calculating the same following equation shall be used.

Payout annuity formula=Po=d(1-(1+r/k)-Nk)/(r/k)

Here,Po is the balance in account at the bigginning of withdrawal

d is the regular withdrawals(here six month withrawal)

r is the annual interest rate(ie 12%=.12)

k is the no.of compounding period in one year

N is the no.of years we plan to withdraw the amount

Here,Po=25000(1-(1+.12/2)-6(2)/(.12/2))

=25000(1-(1+.06)-12)/.06

=25000(1-.50304)/.06

=25000*.49696/.06

=207066

at the age of 18 ,$207066 required in his account

and moreover ,it is required to find out the amount shall be invested in account at the age of 10 to withdraw 25000 every six month from 18 th birth day to 24 th birth day

So,FV=PV*(1+r/2)n*2

  FV=PV(1+(.12/2))16

  207066=PV(1+.06)16

  207066=PV(2.54035)

PV=207066/2.54035

PV=81510

At the age of 10 he must deposit $ 81510 to withdraw $25000 every six month from her 18 th birthday to 24 th birth day.