Manuel bought a $$100,000$ bond with a $5\mathrm{.}4\%$ coupon for $$92,440$ when it had five years remaining to maturity. What was the prevailing market rate at the time Manuel purchased the bond? $($Do not round the intermediate calculations. Round your answer to $2$ decimal places.$)$

Assume that:

Bond interest is paid semiannually.

The bond was originally issued at its face value.

Bonds are redeemed at their face value at maturity.

Market rates of return and yields to maturity are compounded semiannually.

Prevailing market rate

$\%$ compounded semiannually.