Question
A given initial capital in simple interest at the annual rate and for 27 months produced the accumulated capital of 6600 um if the same capital had been invested at the same rate but during 28 months the said accumulated capital would be increased in an amount corresponding to 0.75% of the initial capital Calculate the initial capital and the annual rate at which it was invested
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Answer to a math question A given initial capital in simple interest at the annual rate and for 27 months produced the accumulated capital of 6600 um if the same capital had been invested at the same rate but during 28 months the said accumulated capital would be increased in an amount corresponding to 0.75% of the initial capital Calculate the initial capital and the annual rate at which it was invested
Hank
4.897 Answers
Este é um problema de juros simples, que é calculado pela fórmula:
I = Prt
onde I são os juros, P é o principal, r é a taxa e t é o tempo.
Seja P o capital inicial er a taxa anual. Então, de acordo com as informações fornecidas, temos:
6600 = P + P \vezes r \vezes \frac{27}{12}
e
6600 + 0,0075P = P + P \vezes r \vezes \frac{28}{12}
Resolvendo essas duas equações simultaneamente, obtemos:
P = 5488.56548
e
r = 0,9
Portanto, o capital inicial foi de 5.488,57 um e a taxa anual foi de 9%.
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