Solve 0.08(1+0.08)^20/(1+0.08)^20-1

$$\frac { 0.08 ( 1 + 0.08 ) ^ { 20 } } { ( 1 + 0.08 ) ^ { 20 } - 1 }$$

Evaluate

$$\frac{42391158275216203514294433201}{416202640718586514189300532200}\approx 0.101852209$$

Solution Steps

Add 1 and 0.08 to get 1.08.

$$\frac{0.08\times 1.08^{20}}{\left(1+0.08\right)^{20}-1}$$

Calculate 1.08 to the power of 20 and get 4.6609571438493020524332763932966808190976.

$$\frac{0.08\times 4.6609571438493020524332763932966808190976}{\left(1+0.08\right)^{20}-1}$$

Multiply 0.08 and 4.6609571438493020524332763932966808190976 to get 0.372876571507944164194662111463734465527808.

$$\frac{0.372876571507944164194662111463734465527808}{\left(1+0.08\right)^{20}-1}$$

Add 1 and 0.08 to get 1.08.

$$\frac{0.372876571507944164194662111463734465527808}{1.08^{20}-1}$$

Calculate 1.08 to the power of 20 and get 4.6609571438493020524332763932966808190976.

$$\frac{0.372876571507944164194662111463734465527808}{4.6609571438493020524332763932966808190976-1}$$

Subtract 1 from 4.6609571438493020524332763932966808190976 to get 3.6609571438493020524332763932966808190976.

$$\frac{0.372876571507944164194662111463734465527808}{3.6609571438493020524332763932966808190976}$$

Expand \frac{0.372876571507944164194662111463734465527808}{3.6609571438493020524332763932966808190976} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000.

$$\frac{372876571507944164194662111463734465527808}{3660957143849302052433276393296680819097600}$$

Reduce the fraction \frac{372876571507944164194662111463734465527808}{3660957143849302052433276393296680819097600} to lowest terms by extracting and canceling out 8796093022208.

$$\frac{42391158275216203514294433201}{416202640718586514189300532200}$$

Factor

$$\frac{3 ^ {60}}{11 \cdot 13 \cdot 181 \cdot 677 \cdot 1151 \cdot 463741 \cdot 222495246481 \cdot 2 ^ {3} \cdot 5 ^ {2}} = 0.10185220882315063$$