A little knowledge: 72. 115 rule, compound interest, and fixed compound interest calculation formula

Calculate the formula of compound interest: the annual profit is X %, and the profit after N years is (1 + x %) ^ n.
Excel can be used for automatic calculation. The formula is: = power (1.08, n), 1.08 is 1 + year growth, and N is the number of years.
Simple Estimation Method:
72 rule-used to calculate how many years of investment is required to double the given annual income.
For example, if the annual income is 5%, 72/5 = 14.4. That is, the investment can be doubled in about 14.4 years (if the standard formula is used to calculate the result as 14.2 years); if the annual income is 7%, 72/7 = 10.3, that is, the investment of about 10.3 years can be doubled (calculated by the formula as 10.24 years). If the annual income is 10%, 72/10 = 7.2 is used, that is, the investment of about 7.2 million years can be doubled (calculated as 7.27 million years )......
That is, if the annual income is X %, the expected year for doubling is 72/X, which makes it easy to calculate that if the annual income is 12%, the expected year for doubling is 6 years; if the revenue is 15%, the doubling will take five years. If the profit is 12%, it will take three times in 18 years, that is, eight times.
The 115-72 rule is the doubling of computing time, while the 115 rule is the calculation of 1 to 3, that is, the doubling of time. The calculation method is the same. Using 115/X is the year when the principal is changed to three times. For example, if the income is 10%, the time for 1000 yuan to change to 3000 yuan is 115/10 = 11.5 years.
72. The 115 rule is an estimation. for compound interest with a large or small annual growth rate, the error is relatively large.
Fixed investment compound interest calculation: fixed investment every month. If the annual fixed investment amount is m, the annual growth rate is X, and the total market value after N years is:
M + M * (1 + x) ^ 1 + M * (1 + x) ^ 2 + M * (1 + x) ^ 3 + M * (1 + x) ^ 4 ........ + M * (1 + x) ^ n
The simplified formula is the sum of an proportional series: M * (1 + x) ^ (n + 1)-1)/x
For example, if you invest 12000 yuan a year (monthly investment of 1000 yuan), the annual growth rate is 15%, M = 12000, x = 15%, n = 10,
The total amount after 10 years is 12000*(1 + 15%) ^ (10 + 1)-1)/15% = 12000 (1.15 ^ 11-1)/0.15 = 292191.31, the only thing that should be noted is that this includes 11th years and then 12000 yuan, excluding 11th years of investment and the last M.