IRR Double Your Money: According to the given rule, what is the approximate IRR to double money in N years?

IRR Double Your Money: According to the given rule, what is the approximate IRR to double money in N years?

• A. 75% / N
• B. 100% / N
• C. 50% / N
• D. 25% / N

Answer: (A)

The idea here is a quick way to estimate the annual IRR needed to double your money with compounding. If you earn an annual rate r, after N years you have (1 + r)^N. Setting that roughly equal to 2 for doubling gives N ln(1 + r) ≈ ln 2. For small r, ln(1 + r) ≈ r, so N r ≈ ln 2, which leads to r ≈ ln(2)/N ≈ 0.693/N. To make mental math easier, this rule is often memorized as roughly 75% divided by N. That gives a handy estimate close to the true value, since the exact rate satisfies r = 2^(1/N) − 1, which for small N is near 0.75/N. For example, over 4 years, the rule suggests about 18.75% per year, while the exact calculation is 2^(1/4) − 1 ≈ 18.9%.

The idea here is a quick way to estimate the annual IRR needed to double your money with compounding. If you earn an annual rate r, after N years you have (1 + r)^N. Setting that roughly equal to 2 for doubling gives N ln(1 + r) ≈ ln 2. For small r, ln(1 + r) ≈ r, so N r ≈ ln 2, which leads to r ≈ ln(2)/N ≈ 0.693/N. To make mental math easier, this rule is often memorized as roughly 75% divided by N. That gives a handy estimate close to the true value, since the exact rate satisfies r = 2^(1/N) − 1, which for small N is near 0.75/N. For example, over 4 years, the rule suggests about 18.75% per year, while the exact calculation is 2^(1/4) − 1 ≈ 18.9%.