(1+15%)^12-1/15% eching

$$\frac { ( 1 + 15 \% ) ^ { 12 } - 1 } { 15 \% }$$

Baholash

$$\frac{5939541477340107}{204800000000000}\approx 29,00166737$$

Yechim qadamlari

\frac{15}{100} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\left(1+\frac{3}{20}\right)^{12}-1}{\frac{15}{100}}$$

\frac{23}{20} olish uchun 1 va \frac{3}{20}'ni qo'shing.

$$\frac{\left(\frac{23}{20}\right)^{12}-1}{\frac{15}{100}}$$

12 daraja ko‘rsatkichini \frac{23}{20} ga hisoblang va \frac{21914624432020321}{4096000000000000} ni qiymatni oling.

$$\frac{\frac{21914624432020321}{4096000000000000}-1}{\frac{15}{100}}$$

\frac{17818624432020321}{4096000000000000} olish uchun \frac{21914624432020321}{4096000000000000} dan 1 ni ayirish.

$$\frac{\frac{17818624432020321}{4096000000000000}}{\frac{15}{100}}$$

\frac{15}{100} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{17818624432020321}{4096000000000000}}{\frac{3}{20}}$$

\frac{17818624432020321}{4096000000000000} ni \frac{3}{20} ga bo'lish \frac{17818624432020321}{4096000000000000} ga k'paytirish \frac{3}{20} ga qaytarish.

$$\frac{17818624432020321}{4096000000000000}\times \frac{20}{3}$$

\frac{5939541477340107}{204800000000000} hosil qilish uchun \frac{17818624432020321}{4096000000000000} va \frac{20}{3} ni ko'paytirish.

$$\frac{5939541477340107}{204800000000000}$$

Omil

$$\frac{3 \cdot 7 \cdot 13 \cdot 43 \cdot 67 \cdot 97 \cdot 181 \cdot 463 \cdot 929}{2 ^ {22} \cdot 5 ^ {11}} = 29\frac{341477340107}{204800000000000} = 29,00166736982474$$