consider the following two financial assets:

$1)$ a US stock that is expected to pay a dividend of $50\%$ next year, $$60$ in year $2$ with dividend growth expected to be $3\%$ per annum thereafter;

$2)$ a US corporate bond with an annual coupon rate of $5\%,$ par $($face$)$ value if $$1000,$ and maturity in $3$ years$-$time

a$)$ If the required return on similar US equities is $10\%$ and on similar US bonds is $5\%,$ calculate the value of the US stock and the US bond

b$)$ Using the data given above and assuming an annual discount rate, calculate the Macauley duration of the US bond

c$)$ Briefly describe the factors that affect Macauley duration and explain why Macauley duration is a useful measure for a bond investor?