Question

Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life. At what amount could this loan be sold for to another bank if loans of similar quality carried an 8.5 percent interest rate? That is, what would be the present value of this loan?

Answer 1

Answer:

1,000

and 1,000

Explanation:

The loan rate is 8,5%

85/1000 = 8.5

The market rate is 8.5

So the loan should be sold at 1,000 which is the face value of the loan, because there is no difference between the market rate and the loan rate.

This can be calculated anyway to prove it:

present value of the annuity of $85 during 8 years at 8.5% market rate

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 85

time 8

rate 0.085

$85 \times \frac{1-(1+0.085)^{-8} }{0.085} = PV$

PV $479.3306

Present value of the maturity date:

$\frac{Maturity}{(1 + rate)^{time} } = PV$

Maturity 1000

time 8

rate 0.085

$\frac{1000}{(1 + 0.085)^{8} } = PV$

PV  $520.6694

Total present value

PV c $479.3306

PV m  $520.6694

Total $1,000.0000