Paul expects to receive payments of $1,000$ at the end of each year for $5$ years, with payments beginning one year from now. Howard expects to receive payments of $1,000$ at the end of each year for $10$ years, also with payments beginning one year from now. With an annual effective interest rate of $i\%$ for both accounts, the present value of Howard's payments is $50\%$ more than the present value of Paul's payments.

Determine $i.$

Possible Answers

$10\mathrm{.}87\%$

$11\mathrm{.}87\%$

$12\mathrm{.}87\%$

$13\mathrm{.}87\%$

$14\mathrm{.}87\%$