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UPX bank is selling a security that makes equal annual payments of $7,000 with the first payment 3 years from today and the last payment 9 years from today. Find the price of the security today if the interest rate is 5.1%.

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facundobuzzetti

Answer:

The security is worth $30,570.77.-

Explanation:

Giving the following information:

Annual payment (3 to 9)= $7,000

Interest rate= 5.1%

First, we need to determine the value of the security 3 years from now:

FV= {A*[(1+i)^n-1]}/i

A= annual payment

FV= {7,000*[(1.051^6) - 1]} / 0.051

FV= $47,833.35

PV= FV/(1+i)^n

PV= 47,833.35 / 1.051^6

PV= $35,490.70

The value of the security in 3 years is $35,490.70.

Now, the present value:

PV= 35,490.70 / 1.051^3

PV= $30,570.77

The security is worth $30,570.77.-