Solve 1.03^2-1/0.225*1.025^30*8000+3000*1.025^circ=?

$$\frac { 1.03 ^ { 2 } - 1 } { 0.225 } \cdot 1.025 ^ { 30 } \cdot 8000 + 3000 \cdot 1.025 ^ { \circ } = ?$$

Evaluate

$$\frac{823286798665715258984496864741052129276038642651803}{108086391056891904000000000000000000000000000000}\approx 7616.932997905$$

Solution Steps

Calculate 1.03 to the power of 2 and get 1.0609.

$$\frac{1.0609-1}{0.225}\times 1.025^{30}\times 8000+3000\times 1.025$$

Subtract 1 from 1.0609 to get 0.0609.

$$\frac{0.0609}{0.225}\times 1.025^{30}\times 8000+3000\times 1.025$$

Expand \frac{0.0609}{0.225} by multiplying both numerator and the denominator by 10000.

$$\frac{609}{2250}\times 1.025^{30}\times 8000+3000\times 1.025$$

Reduce the fraction \frac{609}{2250} to lowest terms by extracting and canceling out 3.

$$\frac{203}{750}\times 1.025^{30}\times 8000+3000\times 1.025$$

Calculate 1.025 to the power of 30 and get 2.097567579081791436203112708047991607979702638129594627347529467442655004560947418212890625.

$$\frac{203}{750}\times 2.097567579081791436203112708047991607979702638129594627347529467442655004560947418212890625\times 8000+3000\times 1.025$$

Convert decimal number 2.097567579081791436203112708047991607979702638129594627347529467442655004560947418212890625 to fraction \frac{2418330769289520463963038742566759257517431737201}{10000000000}. Reduce the fraction \frac{2418330769289520463963038742566759257517431737201}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{203}{750}\times \frac{2418330769289520463963038742566759257517431737201}{1152921504606846976000000000000000000000000000000}\times 8000+3000\times 1.025$$

Multiply \frac{203}{750} times \frac{2418330769289520463963038742566759257517431737201}{1152921504606846976000000000000000000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{203\times 2418330769289520463963038742566759257517431737201}{750\times 1152921504606846976000000000000000000000000000000}\times 8000+3000\times 1.025$$

Do the multiplications in the fraction \frac{203\times 2418330769289520463963038742566759257517431737201}{750\times 1152921504606846976000000000000000000000000000000}.

$$\frac{490921146165772654184496864741052129276038642651803}{864691128455135232000000000000000000000000000000000}\times 8000+3000\times 1.025$$

Express \frac{490921146165772654184496864741052129276038642651803}{864691128455135232000000000000000000000000000000000}\times 8000 as a single fraction.

$$\frac{490921146165772654184496864741052129276038642651803\times 8000}{864691128455135232000000000000000000000000000000000}+3000\times 1.025$$

Multiply 490921146165772654184496864741052129276038642651803 and 8000 to get 3927369169326181233475974917928417034208309141214424000.

$$\frac{3927369169326181233475974917928417034208309141214424000}{864691128455135232000000000000000000000000000000000}+3000\times 1.025$$

Reduce the fraction \frac{3927369169326181233475974917928417034208309141214424000}{864691128455135232000000000000000000000000000000000} to lowest terms by extracting and canceling out 8000.

$$\frac{490921146165772654184496864741052129276038642651803}{108086391056891904000000000000000000000000000000}+3000\times 1.025$$

Multiply 3000 and 1.025 to get 3075.

$$\frac{490921146165772654184496864741052129276038642651803}{108086391056891904000000000000000000000000000000}+3075$$

Convert 3075 to fraction \frac{332365652499942604800000000000000000000000000000000}{108086391056891904000000000000000000000000000000}.

$$\frac{490921146165772654184496864741052129276038642651803}{108086391056891904000000000000000000000000000000}+\frac{332365652499942604800000000000000000000000000000000}{108086391056891904000000000000000000000000000000}$$

Since \frac{490921146165772654184496864741052129276038642651803}{108086391056891904000000000000000000000000000000} and \frac{332365652499942604800000000000000000000000000000000}{108086391056891904000000000000000000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{490921146165772654184496864741052129276038642651803+332365652499942604800000000000000000000000000000000}{108086391056891904000000000000000000000000000000}$$

Add 490921146165772654184496864741052129276038642651803 and 332365652499942604800000000000000000000000000000000 to get 823286798665715258984496864741052129276038642651803.

$$\frac{823286798665715258984496864741052129276038642651803}{108086391056891904000000000000000000000000000000}$$