Future va u You h e S000 to \"\'vest r you cen een 14% nt · t, about how lor doe
ID: 2817872 • Letter: F
Question
Future va u You h e S000 to "'vest r you cen een 14% nt · t, about how lor does a ror you' 900 "wysin en ow to $1.800? If thernualinterest rate s 14% te number of years ktakesto double your money is years Round to two decimal places lt thannual i terast rata ust halt at 7% tha nur ar at yaa s t takas to do bl your money O years Round to t o daclmal iacas M hali the interet rae, do take cxactly twice along to double your mony? Select the best anwer telow.) O A. Na, it takes sightly less than twice 5 long io double your money because the money accumulated faster over longer timc pcriod CNa, ht takes more than wica as long to doubla your manay bacausa tha manay mut ba accumulahed avan langar at halt tha Inarast rata uppo " the inty eel 8le S lusl helf that 7%. AI hsr nte el e do s i lek 8cl 1 -ss l ng k double your nre ? Why o why not? How lon does it teke? D. Yes, it takes exactly twice as long 10 double your money because the number of time periods is inearly related 10 the interest rate.Explanation / Answer
Investment amount = 900 = PV
Future value of the investment = FV = 1800
Interest rate = 14%
FV = PV * (1+r)^n
1800 = 900(1+0.14)^n
(1+0.14)^n = 1800/900
(1.14)^n = 2
n = ln 2/ln 1.14
n = 5.29005956
If the interest rate is half of 14% (i.e) 7%, then
1800 = 900*(1+0.07)^n
n = ln (2) /ln (1.07)
n = 10.2447684
When the interest rate is half the number of years to convert the investment of 900 to 1800 is doubling. That is when the interest rate is 14%, the number of years took was 5 ( rounded), and when the interest rate is 7%, the number of years it takes is 10 years(rounded)
The answer is D.
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