A friend wants to borrow money from you. He states that he will pay you $4,700 every 6 months for 9 years with the first payment exactly 2 years and six months from today. The interest rate is an APR of 5.8 percent with semiannual compounding. What is the value of the payments today

PV= $56,508.47

Explanation:

Giving the following information:

Semmiannual payment= $4,700

Number of periods (n)= 9*2= 18 semesters

Interest rate= 0.058/2= 0.029

First, we need to calculate the value of the payments at the moment of the first payment:

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

A= Semmiannual payment

PV= 4,700*{(1/0.029) - 1/[0.029*(1.029^18)]}

PV= $65,191.42

Now, the present value using the following formula:

PV= FV / (1 +i)^n

n= 2.5*2= 5 semesters

PV= 65,191.42 / (1.029^5)

PV= $56,508.47