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Interest rate with annuity. What are you getting in terms of interest rate if you are...

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?

Solutions

Expert Solution

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.

jeff jeffy answered 2 years ago
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