A 13-year annuity pays $1,100 per month, and payments are made at the end of each...

A 13-year annuity pays $1,100 per month, and payments are made at the end of each month. The interest rate is 9 percent compounded monthly for the first five years and 6 percent compounded monthly thereafter.

What is the present value of the annuity?

Solutions

Expert Solution

first we need to find the present value of $1,100 annuity for the remaining 7 years.

Rate = 6% / 12 = 0.5%

Number of periods = 8 * 12 = 96

Present value at year 5 = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value at year 5 = 1,100 * [1 - 1 / (1 + 0.005)⁹⁶] / 0.005

Present value at year 5 = 1,100 * 76.095218

Present value at year 5 = $83,704.74008

Rate = 9% / 12 = 0.75%

Number of periods = 5 * 12 = 60

Present value = Future value / (1 + r)ⁿ

Present value today = 83,704.74008 / (1 + 0.0075)⁶⁰

Present value today = 83,704.74008 / 1.565681

Present value today = $53,462.19318

Present value of annuity = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value of annuity = 1,100 * [1 - 1 / (1 + 0.0075)⁶⁰] / 0.0075

Present value of annuity = 1,100 * 48.173374

Present value of annuity = $52,990.71087

Total present value of the annuity = $52,990.71087 + $53,462.19318

Total present value of the annuity = $106,452.90

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

A 13-year annuity pays $1,400 per month, and payments are made at the end of each...

A 13-year annuity pays $1,400 per month, and payments are made at the end of each month. The interest rate is 12 percent compounded monthly for the first Five years and 11 percent compounded monthly thereafter. Required: What is the present value of the annuity? A) $1,343,944.86 B) $109,755.50 C) $111,995.40 D) $152,061.20 E) $114,235.31

A 15-year annuity pays $1,500 per month, and payments are made at the end of each...

A 15-year annuity pays $1,500 per month, and payments are made at the end of each month. If the interest rate is 10 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity?

A 17-year annuity pays $1,600 per month, and payments are made at the end of each...

A 17-year annuity pays $1,600 per month, and payments are made at the end of each month. The interest rate is 11 percent compounded monthly for the first six years and 9 percent compounded monthly thereafter. What is the present value of the annuity? $153,407.29 $150,339.14 $156,475.43 $217,830.03 $1,840,887.45

A 20-year annuity pays $2,100 per month, and payments are made at the end of each...

A 20-year annuity pays $2,100 per month, and payments are made at the end of each month. If the interest rate is 11 percent compounded monthly for the first ten years, and 7 percent compounded monthly thereafter, what is the present value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

A 12-year annuity pays $1,400 per month, and payments are made at the end of each...

A 12-year annuity pays $1,400 per month, and payments are made at the end of each month. The interest rate is 11 percent compounded monthly for the first six years and 10 percent compounded monthly thereafter. What is the present value of the annuity?

A 18-year annuity pays $1,300 per month, and payments are made at the end of each...

A 18-year annuity pays $1,300 per month, and payments are made at the end of each month. The interest rate is 12 percent compounded monthly for the first six years and 10 percent compounded monthly thereafter. What is the present value of the annuity?

17. A 19-year annuity pays $1,300 per month, and payments are made at the end of...

17. A 19-year annuity pays $1,300 per month, and payments are made at the end of each month. The interest rate is 7 percent compounded monthly for the first Six years and 5 percent compounded monthly thereafter. Required: What is the present value of the annuity? Multiple Choice $177,689.68 $225,152.39 $170,721.46 $2,090,466.81 $174,205.57 18. Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your...

A 15-year annuity pays $1,000 per month, and payments are madeat the end of each...

A 15-year annuity pays $1,000 per month, and payments are made at the end of each month. The interest rate is 15 percent compounded monthly for the first six years and 14 percent compounded monthly thereafter. What is the present value of the annuity?Multiple Choice$108,515.59$72,323.18$867,878.16$70,876.72$73,769.64

A 20-year annuity pays $1,450 per month, and payments are madeat the end of each...

A 20-year annuity pays $1,450 per month, and payments are made at the end of each month. If the interest rate is 11 percent compounded monthly for the first ten years, and 7 percent compounded monthly thereafter, what is the present value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Sumeet has a 13 year annuity that pays at the end of each year. The first...

Sumeet has a 13 year annuity that pays at the end of each year. The first payment is $2000 and the payments grow by R = 5% per year. Interest rates are r = 6% annually. a) How much is Sumeet's annuity worth? Consider the following two options: Option A: An annuity with the same number of payments, only each payment is twice the payment of his current annuity. Option B: An annuity where the initial payment is the same...

Subjects