Question

a 17-year annuity pays $1,100 per month, and payments are made at the end of each month. The interest rate is 16 percent compounded monthly for the first 6 years and 13 percent compounded monthly thereafter. What is the present value of the annuity

Answer 1

Answer:

The present value of the annuity is $73,091.50

Explanation:

Use the following formula to calculate the present value of the annuity

Present value of annuity = ( Annuity Payment x Annuity factor for first 6 years ) + [ ( Annuity Payment x Annuity factor for after 6 years ) x Present value factor  for 6 years ]

Where

Annuity Payment = $1,000

Annuity factor for first 6 years = 1 - ( 1 + 16%/12 )^-(6x12) / 16%/12 = 46.10028344

Annuity factor for after 6 years = 1 - ( 1 + 13%/12 )^-((17-6)x12) / 13%/12 = 70.0471029820

Present value factor for 6 years = ( 1 + 16%/12)^-(6x12) = 0.385329554163

Placing values in the formula

Present value of annuity = ( $1,000 x 46.10028344 ) + [ ( $1,000 x 70.0471029820 ) x 0.385329554163 ]

Present value of annuity = $46,100.28 + $26,991.22

Present value of annuity = $73,091.50