Assuming that the rate of interest is i=a, an investment of 1 will increase to 4 after n years. Find the accumulated value of 1 after n years, when the rate of interest is i'=3a. (hint: the answer is 64)
(I already know that (1+a)^n=4, (1+3a)^n=x and I don't know what to do after that because I am a beginner. The exercise doesn't clarify that it is a compound interest, but we have said earlier that when it is not clarified it's compound.)
I hope I understand your question correctly. If we assume compound continuously ($A=Pe^{rt}$), then with rate $a$ and principal $1$, we arrive at $1e^{4a}=4$ from the given. When we change the rate into $3a$, then the formula becomes $1e^{12a}$ (literally "replace" $a$ by $3a$), which is $1(e^{{4a}})^3$. From here the $64$ logically follows by rules of exponents.