Finance problem about funds

[Kagankarakoc]

A fund with 5000 USD called A is growing with an "instant interest rate" of δ= 1/(12-t). "0<=t<=12"
Another fund with 5000 USD called B is growing during 4 years with an annual nominal interest rate %4 which can be convertible to "6 monthly rates" (6 month period). (%4 /2 =%2) And for following years this fund is growing with an annual interest rate "i"
At the end of 5th year the values of the funds (the amounts) A and B are equal. What is the value of the interest rate "i" ???

 

[Kagankarakoc]

I found a solution to this also it is a little bit complicated, if you don't understand some parts, I can get explain.

 

[Kagankarakoc]

What I didn't understand was the English translation....

ok let me, I will only explain Fund A, because u had no problem with Fund B

Fund A with 5000 USD is growing with an "instantaneous interest rate"of δ(t)= 1/(12-t). "0<=t<=12"

[The instantaneous rate, which is obtained when ∆t is infinitesimally small. The instantaneous rate is also called the force of interest which is the instantaneous rate of increase of the accumulated amount, a'(t), as a percentage of the accumulated amount at time "t", a(t).] [ a'(t) is derivative of a(t) "accumulated amount" with respect to "t"(time)]



Another fund with 5000 USD called B is growing during 4 years with an annual nominal interest rate %4 which can be convertible to "6 monthly rates" (6 month period). (%4 /2 =%2) And for following years this fund is growing with an annual interest rate "i"
At the end of 5th year the values of the funds (the amounts) A and B are equal. What is the value of the interest rate "i" ???