Question

You want to make an investment in a continuously compounding account over a period of 20 years. What interest rate is required for your investment to double in that time period? Round the logarithm value to the nearest hundredth and the answer to the nearest tenth.You want to make an investment in a continuously compounding account over a period of 20 years. What interest rate is required for your investment to double in that time period? Round the logarithm value to the nearest hundredth and the answer to the nearest tenth

Answer 1

2 = e^(r * 20)

ln(2) = 20 r

Answer 2

P = Po*e^rt = 2Po.
Po*e^rt = 2Po.
e^rt = 2,
rt*Lne = Ln2,
r*t = Ln2/Lne = 0.693,
r = 0.693/t = 0.693/20 = 0.035 = 3.5 %.