Sadeeq wants to save for a down payment on a house and plans to deposit $700 every month into an annuity for the next 7 years. If the annuity interest rate is 5 percent per year, what is the present value of the annuity? Round your answer to the nearest hundredth.(1 point) Responses 35,500.12 35,500.12 49,526.28 49,526.28 110,220.40 110,220.40 52,000.30
The formula to calculate the present value of an annuity is:
PVA = Pmt * [(1 - (1 + r)^(-n)) / r]
where:
PVA = Present value of the annuity
Pmt = Monthly deposit amount ($700)
r = Interest rate per period (5% per year / 12 months = 0.4167% per month)
n = Number of periods (7 years * 12 months/year = 84 months)
Plugging in the values:
PVA = 700 * [(1 - (1 + 0.05/12)^(-84)) / (0.05/12)]
PVA = 700 * [(1 - (1.004167)^(-84)) / (0.004167)]
PVA = 700 * [(1 - 0.261678) / 0.004167]
PVA = 700 * (0.738322 / 0.004167)
PVA = 700 * 177.11857
PVA ≈ 123,983.999
Rounding to the nearest hundredth:
PVA ≈ 123,984.00
Therefore, the present value of the annuity is $123,984.00. None of the provided responses match this calculated value.