Suppose that $2-$year interest rates are $4\mathrm{.}6\%$ in the United States and $1\mathrm{.}06\%$ in Japan and that spot exchange rate is USD$/$JPY $=106\mathrm{.}00.$

Suppose that $1$ year later, interest rates are $2\mathrm{.}68\%$ in both countries, while the value of the yen has appreciated to USD$/$JPY $=103\mathrm{.}00.$

a$.$ Benjamin Pinkerton from New York invested in a U$.$S$.2-$year zero$-$coupon bond at the start of the period and sold it after $1$ year.

What was his return?

b$.$ Madame Butterfly from Osaka bought some dollars. She also invested in the one$-$year U$.$S$.$ zero$-$coupon bond and sold it after $1$

year. What was her return in yen?

Note: For all requirements, Do not round intermediate calculations. Enter your answers as a percent rounded to $2$ decimal places.