To the closest year, how long will it take $$200$ to double if it is deposited and earns the following rates? $[$Notes: $(1)$ See the Hint for Problem $4-9.(2)$ This problem cannot be solved exactly with some financial calculators. For example, if you enter PV $200,$ PMT $0,$ FV $400,$ and I $7$ in an HP$-12$C and then press the N key, you will get $11$ years for part a$.$ The correct answer is $10\mathrm{.}2448$ years, which rounds to $10,$ but the calculator rounds up$.$ However, the HP$10$BII gives the exact answer.$]$ a$.7\%$ b$.10\%$ c$.18\%$ d$.100\%$