Answer to Question #249876 in Financial Math for Smiley

Question

if her dad deposits R3570,00

 at the end of every six months for the next four years into a bank account. The account pays 8,5% interest per annum, compounded semi-annually. Her father pays and additional R5550,00

 into the account for every R3570,00

 deposit he makes. The first deposit will be made six months from now. How much money will there be in the account for Aziz to pay for her college expenses?

Answer 1

The Future Value of the annuity is the total value of all the payments which is occurred regularly at a specific time interval at a certain date in the future taken into consideration a specific discount rate or rate of return. The higher the discount rate or rate of interest, the higher will be the future value of the annuity, and the lower the rate of interest or the discount rate, the lower will be the value of the annuity.

Here,

Since the Deposits are made at the end of each year, it will be a case of an ordinary annuity

Semi -Annual Deposit = R3,57,000

Additional Semi -Annual Deposit = R5,55,000

$Total\space Semi −Annual\space Deposit= Semi − Annual\space Deposit +Additional\space Semi− Annual Deposit\\Total\space Semi −Annual\space Deposit=R3,57,000+R5,55,000R912,000\\Total\space Semi −Annual\space Deposit=R912,000$

Interest rate = 8.5% per annum compounded semi-annually

Semi-Annual Interest rate =0.085/2 = 0.0425

Time Period = 4 years 

Semi -Annual Periods = 4 years *2 = 8 Semi -Annual Periods

Using the Future Value of Annuity Formula

$FV\space of\space Annuity=P[\frac{(1+r)^n-1}{r}]$

where P=Periodic payment

r=rate per period

n=number of periods

$FV\space of\space Annuity=R912,000[\frac{(1+0.0425)^8-1}{0.0425}]$

$FV\space of\space Annuity=R912,000[\frac{0.39511011846}{0.0425}]=R8,478,599.73$

Answer: Total money into the account for Aziz to pay for her college expenses is R8,478,599.73