To calculate the amount needed in the account at the beginning of the 4-year period, we need to find the present value of the annuity payments using the formula for present value of an annuity:
PV = PMT * ((1 - (1 + r)^-n) / r)
Where:
PV = Present Value
PMT = Payment per period (R2,000)
r = Interest rate per period (8% p.a. compounded semi-annually = 8%/2 = 4% per period)
n = Number of periods (4 years = 8 semesters)
Plugging in the values:
r = 4% = 0.04
n = 8
PMT = R2,000
PV = R2,000 * ((1 - (1 + 0.04)^-8) / 0.04)
PV = R2,000 * ((1 - (1.04)^-8) / 0.04)
PV = R2,000 * ((1 - 0.63181) / 0.04)
PV = R2,000 * (0.36819 / 0.04)
PV = R2,000 * 9.20475
PV = R18,409.5
Therefore, the amount needed in the account at the beginning of the 4-year period to make these payments possible is R18,409.5.
A bursary fund pays R2 000 at the beginning of each semester for a period of 4 years to a Kovsie student. The account from which these payments are made earns interest at 8% p.a. compounded semi-annually. What amount was needed in the account at the beginning of the 4-year period to make these payments possible?
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