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)
35,500.12
49,526.28
110,220.40
52,000.30
In this case, Sadeeq is depositing $700 every month for 7 years.
The first step is to calculate the total number of months in 7 years: 7 years x 12 months/year = 84 months
Next, we can use the formula for calculating the present value of an annuity:
PV = Pmt x [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value
Pmt = Payment per period ($700/month)
r = Interest rate per period (5% per year / 12 months = 0.41667% per month)
n = Total number of periods (84 months)
PV = $700 x [(1 - (1 + 0.05/12)^-84) / (0.05/12)] = $49,526.28
Therefore, the present value of the annuity is $49,526.28. (rounded to the nearest hundredth)