# Interest rate on loan for purchasing Sterling bond

I am struggling trying to find out where they get the $8$% interest rate for the loan you make to purchase the Sterling Bond in the following strategy:

Problem:

Suppose that $A(0)$ = $100$ and $A(1)$ = $105$ dollars, the present price of pound sterling is $S(0)$ = $1.6$ dollars, and the forward price is $F = 1.50$ dollars to a pound with delivery date $1$. How much should a sterling bond cost today if it promises to pay $£100$ at time $1$? Hint: The forward contract is based on an asset involving negative carrying costs (the interest earned by investing in sterling bonds).

Strategy:

Suppose that a sterling bond promising to pay $£100$ at time $1$ is selling for $x$ pounds at time $0$. To find $x$ consider the following strategy.

At time $0$:

• Borrow $1.6x$ dollars and change the sum into $x$ pounds.

• Purchase a sterling bond for $x$ pounds.

• Take a short forward position to sell $£100$ for $\$1.50$to a pound with delivery date$1$. Then, at time$1$: • Cash the bond, collecting$£100$. • Close the short forward position by selling$£100$for$\$150$.

• Repay the cash loan with interest, that is, $1.68x$ dollars in total.

## 1 Answer

First, it's not a 8% loan. The .08 interest on 1.6 is 5%. It appears that it is coming from the $A (1) = 105$.