Question

What is TIME FOR A LUMP SUM TO DOUBLE

How long will it take $200 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places.

1. 6%.

   ? year(s)

2. 10%.

   ? year(s)

3. 20%.

   ? year(s)

4. 100%.

   ? year(s)

Answer 1

In this question, FV = 2 * $200 = $400

a) $400 = $200 * (1 + 6%)ⁿ

2 = 1.06ⁿ

Taking log of both sides,

LN(2) = n * LN(1.06)

0.693147 = n * 0.058269

n = 11.90 years

b) $400 = $200 * (1 + 10%)ⁿ

2 = 1.10ⁿ

Taking log of both sides,

LN(2) = n * LN(1.10)

0.693147 = n * 0.09531

n = 7.27 years

c) $400 = $200 * (1 + 20%)ⁿ

2 = 1.20ⁿ

Taking log of both sides,

LN(2) = n * LN(1.20)

0.693147 = n * 0.182322

n = 3.80 years

d) $400 = $200 * (1 + 100%)ⁿ

2 = 1.1ⁿ

Taking log of both sides,

LN(2) = n * LN(1.1)

0.693147 = n * 0.693147

n = 1 year