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.
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
1 answer
1 answer