Help on investment math?!?

Question

PROBLEM: A principal of 10,000 was invested at a certain effective rate of interest for five years. Thereafter, money was allowed to accumulate further for the next five years, as long as the effective rate becomes double. It is expected that the accumulated value at the end of the term will be 22,000. What was the original effective rate?

Pls. use the formula:

F=P(1+j/m)^mt

where: F=final accumulated value;

P=principal;

j=rate of interest per year;

m=no. of conversion periods;

t=term of investment expressed in years

Given: (1st five years) P=10,000 ; m=1 ; t=5 ; j=j ; F=?

(2nd five years) P=? ; m=1 ;t=5 ; j=2j ; F=22,000

...any little help for the solution will be appreciated. Thanks! God bless.. :)

Answer 1

I have to tell you that I don't understand the question -- and I have a PhD in Finance.  Your interpretation that the rate for the second five years is how I also interpreted it -- but I'm not sure that is what is meant.

If so -- then you get:

22000 = 10000*(1+j)^5 * (1+2*j)^5

This implies that (2.2)^(1/5) = [(1+j)*(1+2j)=1+3j+j^2

You can use the quadratic equation to solve for j.