Considering the situation described above, what would be the present value of this loan is $1,000.
This is explained below:
Given that the loan interest rate is $85 85/1000 = 8.5
Then the market interest rate is => 8.5 percent
Therefore, given that there is no difference between the market rate and the loan rate, then the loan is expected to be sold at $1,000 which is the face value of the loan.
To prove it, we have the following:
PV of the annuity of $85 during 8 years at an 8.5% market rate
C => 85
Time => 8
Rate => 0.085
C × { [1 - ( 1+ r ) ] ^-time } ÷ rate = PV
85 × [1 - (1 + 0.085)^-8] ÷ 0.085 = PV
PV =. $479.3306
Present value of the maturity date:
Maturity 1000
Time => 8
Rate => 0.085
Maturity ÷ (1+rate)^rate = PV
1000 ÷ (1+0.085)^8 = PV
PV => $520.6694
Therefore, the Total present value
=> PV c $479.3306 + PV m $520.6694
=> Total $1,000.
Hence, in this case, it is concluded that the correct answer is $1,000.
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