Question

Company X has a 5 year $1 million loan that pays interest every six months at a floating rate that is adjusted every six months and is currently at 3% (quoted as an annual rate). If this rate is expected to increase every six months by .25%, what is a fair interest rate (annualized) for the fixed side of a fixed for floating swap for Company X’s loan?

Answer 1

The fair interest rate (annualized) for the fixed side will be calculated by the concept of CAGR,

$CAGR= (1+R_1)*(1+R_2)*....*(1+R_n)^{1/n}-1$

Year	Interest rate(annual)	Interest (semi annual)
0.5	3%	1.500%
1	3.25%	1.625%
1.5	3.50%	1.750%
2	3.75%	1.875%
2.5	4%	2.000%
3	4.25%	2.125%
3.5	4.50%	2.250%
4	4.75%	2.375%
4.5	5%	2.500%
5	5.25%	2.625%
	CAGR (semi annual)	2.062%	((1+1.5%)*(1+1.625%)*(1+1.75%)*(1+1.875%)*(1+2%)*(1+2.125%)*(1+2.250%)*(1+2.375%)*(1+2.5%)*(1+2.625%))^(1/10)-1
	CAGR (Annual)	4.124%	2.062%*2

annual fixed rate = 4.124%