Question

1. Katie has borrowed 300,000 from Trout Bank. Katie will repay 100,000 of principal at the end of each of the first three years.

Katie will pay Trout Bank a variable interest rate equal to the one-year spot interest rate at the beginning of each year.

Katie would like to have a fixed interest rate so she enters into an interest rate swap with Lily. Under the interest rate swap, Katie will pay a fixed rate to Lily, and Lily will pay a variable rate to Katie. The variable rate will be the same rate that Katie is paying to Trout Bank. The other terms of the swap will mirror the loan that Katie has.

You are given the following spot interest rates:

Time (t)	Spot rate rt
1	4.3%
2	4.6%
3	5.1%
4	5.4%
5	5.6%

Calculate the swap interest rate for Katie’s swap. (A) 4.27%

(B) 4.52%

(C) 4.78%

(D) 5.07%

(E) 5.31%

Answer 1

Calculation of Interest to be paid :-

Year	Opening Outstanding Principal	Repayment	Closing Outstanding Principal	Interest Rate	Interest Amunt
1	300000	100000	200000	4.3%	12900
2	200000	100000	100000	4.6%	9200
3	100000	100000	0	5.1%	5100
	Total				27200

Calculation of Fixed Rate :-

Fixed Rate x (Toatl of Opening Outstanding at Year 1, 2 &3) = Total Interest

So, Fixed Rate x 600000 = 27200

So, Fixed Rate = 4.52% (approx.)

Hence, Swap Interest Rate for Katie's swap would be = 4.52% (Option B)