Five years ago, Grey Ltd issued $$1,000$ denominations with an original maturity of $13$ years and a coupon rate of $12\%.$ Determine the value today of one of these bonds to an investor who requires a $10\%$ rate of return on these securities$.$ $$871\mathrm{.}53$ $$863\mathrm{.}78$ $$900\mathrm{.}65$ $$1,142\mathrm{.}07$ $$1,106\mathrm{.}70$