Solve 30000=A*1-(1+13%)^-10/13%

$$30000 = A \times \frac { 1 - ( 1 + 13 \% ) ^ { - 10 } } { 13 \% }$$

Solve for A

$$A = \frac{33945673899222231484900}{6139916384415956791} = 5528\frac{4.21612617082064 \times 10^{18}}{6.139916384415957 \times 10^{18}} \approx 5528.686674851$$

Steps for Solving Linear Equation

Add 1 and \frac{13}{100} to get \frac{113}{100}.

$$30000=A\times \frac{1-\left(\frac{113}{100}\right)^{-10}}{\frac{13}{100}}$$

Calculate \frac{113}{100} to the power of -10 and get \frac{100000000000000000000}{339456738992222314849}.

$$30000=A\times \frac{1-\frac{100000000000000000000}{339456738992222314849}}{\frac{13}{100}}$$

Subtract \frac{100000000000000000000}{339456738992222314849} from 1 to get \frac{239456738992222314849}{339456738992222314849}.

$$30000=A\times \frac{\frac{239456738992222314849}{339456738992222314849}}{\frac{13}{100}}$$

Divide \frac{239456738992222314849}{339456738992222314849} by \frac{13}{100} by multiplying \frac{239456738992222314849}{339456738992222314849} by the reciprocal of \frac{13}{100}.

$$30000=A\times \frac{239456738992222314849}{339456738992222314849}\times \frac{100}{13}$$

Multiply \frac{239456738992222314849}{339456738992222314849} and \frac{100}{13} to get \frac{1841974915324787037300}{339456738992222314849}.

$$30000=A\times \frac{1841974915324787037300}{339456738992222314849}$$

Swap sides so that all variable terms are on the left hand side.

$$A\times \frac{1841974915324787037300}{339456738992222314849}=30000$$

Multiply both sides by \frac{339456738992222314849}{1841974915324787037300}, the reciprocal of \frac{1841974915324787037300}{339456738992222314849}.

$$A=30000\times \frac{339456738992222314849}{1841974915324787037300}$$

Multiply 30000 and \frac{339456738992222314849}{1841974915324787037300} to get \frac{33945673899222231484900}{6139916384415956791}.

$$A=\frac{33945673899222231484900}{6139916384415956791}$$