Question

Joseph purchased an annuity that had an interest rate of 2.75% compounded semi-annually. It provided her with payments of $2,000 at the end of every month for 7 years. If the first withdrawal is to be made in 3 years and 1 month, how much did she pay for it?

Answer 1

Joseph paid $22,160.76 for the annuity.

Step-by-step explanation:

To calculate the price Joseph paid for the annuity, we can use the formula for the present value of an annuity:

PV = PMT × (1 - (1+r)^(-n)) / r

Where PV is the present value, PMT is the payment per period, r is the interest rate per period, and n is the number of periods.

• First, we need to convert the interest rate from an annual rate to a rate per semi-annual period. The interest rate per semi-annual period is 0.0275 / 2 = 0.01375.
• The number of semi-annual periods over the 7-year period is 7 × 2 = 14.
• The payment per semi-annual period is $2000.
• The present value of the annuity is: PV = 2000 × (1 - (1+0.01375)^(-14)) / 0.01375 = $22,160.76

Therefore, Joseph paid $22,160.76 for the annuity.