Questions on sinking funds
A has agreed to pay rent for 50000 per month for 10 months beginning 5 months from today. Interest rate is 8%per annum. What is the present value of the payment
To calculate the present value of the rental payments, we can use the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value
PMT = Payment amount per period (50000)
r = Interest rate per period (8%/12 months = 0.08/12 = 0.00667)
n = Number of periods (10 months - 5 months = 5 months)
Plugging in the values:
PV = 50000 * [(1 - (1 + 0.00667)^(-5)) / 0.00667]
PV = 50000 * [(1 - (1.00667)^(-5)) / 0.00667]
PV = 50000 * [(1 - (0.993374) / 0.00667]
PV = 50000 * [(1 - 0.993374) / 0.00667]
PV = 50000 * (0.006626 / 0.00667)
PV = 50000 * 0.9944
PV = 49720
Therefore, the present value of the rental payments is approximately 49720.