How long will it take $200 to double if it is deposited and earns the following

Question

How long will it take $200 to double if it is deposited and earns the following rates? Round your answers to the closest year. [Notes: (1) 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-12C and then press the N key, you will get 11 years. The correct answer is 10.2448 years, which rounds to 10, but the calculator rounds up. However, the HP10BII gives the exact answer; (2) If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer.]

5.1%.
year(s)

12.7%.
year(s)

19.2%.
year(s)

100%.
year(s)

Explanation / Answer

$ 200 should become $ 400

If r = 5.1%,

400 = 200*(1.051)^n

n = log2/log1.079

= 13.94 years

If r = 12.7%,

400 = 200*(1.127)^n

n = log2/log1.127 = 5.80 years

If r = 19.2%,
400 = 200*(1.192)^n

n = log2/log1.192 = 3.94 years

If r = 100%,

400 = 200*(2)^n

n = log2/log2 = 1 year

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