Question

Interest rate with annuity. What are you getting in terms of interest rate if you are willing to pay ​$15,000 today for an annual stream of payments of $2,000 for the next 30 years? The next 60 years? The next 150 ​years? ​ Forever?

What are you getting in terms of interest rate if you are willing to pay $15,000 today for an annual stream of payments of $2,000 for the next 30 ​years?

What are you getting in terms of interest rate if you are willing to pay $15,000 today for an annual stream of payments of $2,000 for the next 60 years?

What are you getting in terms of interest rate if you are willing to pay $15,000 today for an annual stream of payments of $2,000 for the next 150 ​years?

What are you getting in terms of interest rate if you are willing to pay $15,000 today for an annual stream of payments of $2,000 ​forever?

Answer 1

1.Information provided:

Present value= $15,000

Annual payment= $2,000

Time= 30 years

The interest rate is calculated by computing the yield to maturity.

The yield to maturity is calculated by entering the below in a financial calculator:

PV= -15,000

PMT= 2,000

N= 30

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 12.9917.

Therefore, the yield to maturity is 12.9917%    13%.

2.Information provided:

Present value= $15,000

Annual payment= $2,000

Time= 60 years

The interest rate is calculated by computing the yield to maturity.

The yield to maturity is calculated by entering the below in a financial calculator:

PV= -15,000

PMT= 2,000

N= 60

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 13.3260.

Therefore, the yield to maturity is 13.3260%    13.33%.

3.Information provided:

Present value= $15,000

Annual payment= $2,000

Time= 150 years

The interest rate is calculated by computing the yield to maturity.

The yield to maturity is calculated by entering the below in a financial calculator:

PV= -15,000

PMT= 2,000

N= 150

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 13.3333.

Therefore, the yield to maturity is 13.3333%    13.33%.

4.Information provided:

Present value= $15,000

Annual payment= $2,000

Time= Perpetuity

Present value of the perpetuity payment= annual payment/discount rate

$15,000= $2,000/ discount rate

discount rate= $2,000/ $15,000

= 0.1333*100

= 13.33%.

In case of any query, kindly comment on the solution.