How much must be invested today if you want to receive R15000 at the beginning of every quarter for the next 11 years from a financial institution that offers 9% effective interest per annum compounded quarterly

Answer 1

The formula to calculate the present value of a series of equal payments is:

PV = PMT * ((1 - (1 + r)^-n) / r)

Where:
PV = Present Value (amount to be invested today)
PMT = Payment amount per quarter (R15000)
r = Interest rate per quarter (9% / 4 = 0.09 / 4 = 0.0225)
n = Total number of quarters (11 years * 4 quarters per year = 44 quarters)

Plugging in the values:

PV = 15000 * ((1 - (1 + 0.0225)^-44) / 0.0225)
PV = 15000 * ((1 - (1.0225)^-44) / 0.0225)
PV = 15000 * ((1 - 0.3646) / 0.0225)
PV = 15000 * (0.6354 / 0.0225)
PV = 15000 * 28.24
PV = R 423,600

Therefore, you would need to invest R423,600 today in order to receive R15,000 at the beginning of every quarter for the next 11 years from a financial institution offering 9% effective interest per annum compounded quarterly.