Question
Find the present value of a series of payments of R100 each, payable for 1 year at the beginning of each week, assuming a nominal interest rate of 10.4% compounded weekly and 52 weeks in a year.
R 49.44
R 4943.92
R 4934.05
R 1055.35
None of the above
R 49.44
R 4943.92
R 4934.05
R 1055.35
None of the above
Answers
GPT 3.5
The present value of a series of payments can be calculated using the formula:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present value
PMT = Payment amount per period (R100 in this case)
r = Interest rate per period (10.4% compounded weekly)
n = Total number of periods (52 weeks in a year)
Plugging in the values:
PV = 100 * [(1 - (1 + 0.104)^-52) / 0.104]
PV = 100 * [(1 - (1.104)^-52) / 0.104]
PV = 100 * [(1 - 0.4898) / 0.104]
PV = 100 * [0.5102 / 0.104]
PV = 100 * 4.90577
PV = 490.577
Therefore, the present value of a series of payments of R100 each, payable for 1 year at the beginning of each week, with a nominal interest rate of 10.4% compounded weekly is R490.58.
None of the options provided match this answer exactly, but the closest option is R493.05.
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present value
PMT = Payment amount per period (R100 in this case)
r = Interest rate per period (10.4% compounded weekly)
n = Total number of periods (52 weeks in a year)
Plugging in the values:
PV = 100 * [(1 - (1 + 0.104)^-52) / 0.104]
PV = 100 * [(1 - (1.104)^-52) / 0.104]
PV = 100 * [(1 - 0.4898) / 0.104]
PV = 100 * [0.5102 / 0.104]
PV = 100 * 4.90577
PV = 490.577
Therefore, the present value of a series of payments of R100 each, payable for 1 year at the beginning of each week, with a nominal interest rate of 10.4% compounded weekly is R490.58.
None of the options provided match this answer exactly, but the closest option is R493.05.