Assuming that the loan principal is P yuan and the monthly repayment amount is X yuan, then:
The annual interest rate of the loan is 0.35 and the monthly interest rate is 0.35/12 = 0.0292;
If the loan term is n months, the monthly interest payable is p × 0.0292; ;
If the monthly repayment amount is X yuan, the remaining loan principal after monthly repayment is P-X+P× 0.0292;
According to the meaning of the question, the monthly repayment amount is 4 thousand yuan, that is, x = 4 thousand yuan;
Therefore, after monthly repayment, the remaining loan principal is P-4000+P× 0.0292;
Finally, according to the principle that the sum of the loan principal plus the monthly repayment is equal to the loan principal, the following equation can be listed and solved: P+n × 4000 = P+n × P × 0.0292.
By modifying the above equation, we can get:
P = n × 4000/( 1 + 0.0292 × n)
According to the meaning of the question, the total repayment amount is: monthly repayment amount × repayment months = 4000 yuan × n.
After P is brought in, you can get:
4000×n = n×4000/( 1+0.0292×n)×n
Simplify to get:
1+0.0292×n = 1/( 1-n/(4000×n))
Finally, it is calculated that n is about 145 months, that is, 12 years and 1 month. So the total loan amount is about: 145 months × 4,000 yuan/month = 580,000 yuan.