You own a portfolio of British assets worth $100,000$ on January$1$st$.$ The portfolio is worth $90,000$ on January $10$th$,$ and youwithdraw $20,000.$ On January $20$th$,$ the value of your portfoliohas gone up to $90,000,$ and you add $50,000.$ On January $31$st$,$your portfolio is worth $145,000.$ Compute the rate of return in January, using the time$-$weighted return method and money$-$weighted return method.