Final answer:
To find the nominal annual rate of interest at which money doubles itself in five years and four months when compounded monthly, we can use the compound interest formula. By rearranging the formula and solving for the interest rate, we find that the nominal annual rate of interest is approximately 8.8906%.
Step-by-step explanation:
To find the nominal annual rate of interest at which money doubles itself in five years and four months when compounded monthly, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount, which is double the original amount of money
- P is the original amount of money
- r is the nominal annual rate of interest
- n is the number of times the interest is compounded per year
- t is the time in years
Since we want to double the money, A will be equal to 2 times P. Plugging in the values, we have:
2P = P(1 + r/12)^(12 * (5 + 4/12))
Simplifying the equation:
2 = (1 + r/12)^(12 * (5 + 4/12))
To solve for r, we need to take the logarithm of both sides:
log(2) = log((1 + r/12)^(12 * (5 + 4/12)))
Using the logarithm property log(a^b) = b * log(a), we can rewrite the equation as:
log(2) = (5 + 4/12) * log(1 + r/12)
Finally, we can solve for r by dividing both sides by (5 + 4/12) * log(1 + r/12) and then multiplying by 12:
r ≈ 12 * [log(2) / (5 + 4/12) * log(1 + r/12)]
Using a calculator, the approximate value of r is 8.8906%. Therefore, the nominal annual rate of interest for money to double itself in five years, four months compounded monthly is approximately 8.8906%.