Question
Find the present value (to the nearest rand) of a series of payments of R1 each, payable for 1 year at the beginning of each week, assuming an effective interest rate of 20% per annum (compounded weekly) and 52 weeks in a year.
R 52
R 48
R 47
R 50
None of the above
R 52
R 48
R 47
R 50
None of the above
Answers
GPT 3.5
R 47
To calculate the present value of a series of payments, we can use the formula for the present value of an ordinary annuity:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = present value
PMT = payment amount (R1)
r = interest rate per period (20%/52 = 0.3846%)
n = total number of payments (52)
Plugging in the values, we get:
PV = 1 * [(1 - (1 + 0.003846)^-52) / 0.003846]
PV = 1 * [(1 - 0.8766) / 0.003846]
PV = 1 * (0.1234 / 0.003846)
PV = 47.009
Therefore, the present value of a series of payments of R1 each, payable for 1 year at the beginning of each week, with an effective interest rate of 20% per annum (compounded weekly) is approximately R47.
To calculate the present value of a series of payments, we can use the formula for the present value of an ordinary annuity:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = present value
PMT = payment amount (R1)
r = interest rate per period (20%/52 = 0.3846%)
n = total number of payments (52)
Plugging in the values, we get:
PV = 1 * [(1 - (1 + 0.003846)^-52) / 0.003846]
PV = 1 * [(1 - 0.8766) / 0.003846]
PV = 1 * (0.1234 / 0.003846)
PV = 47.009
Therefore, the present value of a series of payments of R1 each, payable for 1 year at the beginning of each week, with an effective interest rate of 20% per annum (compounded weekly) is approximately R47.