 # You are considering purchasing a \$1 000 bond with

\$5.00

## You are considering purchasing a \$1 000 bond with

You are considering purchasing a \$1,000 bond with a coupon rate of 9.5%, interest payable annually. You estimate that you will be able to sell the bond at \$1,055 after 3 years.

a. If the current inflation rate is 5% per year, which will continue in the foreseeable future, what would be the real rate of return for your investment?

b. If you have determined an 8% inflation-free MARR, what should be the maximum inflation rate so that your investment would be successful?

a.

First find Nominal Interest Rate Rate of Return

0 = -1000 + (1000*.95) (p/a, i%, 3) + 1055(p/f, i%,3)

Try i = 8 %, where (p/a, 8%, 3) = 2.5770 and (p/f, 8%,3) = .7938 which results in 82.31

Try i = 12% where (p/a, 12%, 3) = 2.4018 and (p/f, 12%,3) = .7117 which results in -20.89

Now interpolate and find nominal interest rate i = 11.19%

Then use the formula (1 + i) = (1 + r) (1 + f) where the nominal rate i = 11.19 %, the inflation rate f = 5%, and find real rate r.

So: (1 + .1119) = (1 + r) (1 + .05) = > r = 5.89%

Real Rate of Return on investment = 5.89%

b.

To find max inflation rate use the formula (1 + i) = (1 + r) (1 + f) where the nominal rate i = 11.19 %, real rate r = 8%, and find the inflation rate f.

So: (1 + .1119) = (1 + .08) (1 + f) => f = 2.95%

To achieve a MARR of 8% the max inflation = 2.95%