Financial Maths question - Calculate number of years over which loan will be repaid A loan has to be repaid over 3n years, through annual repayment installments of 5000 each at an annual interest rate of 10%. Sum of the Interests paid in the (n+1) and that in the 2n+1 year is 5000.
calculate the number of years over which the loan is to be repaid. 
I normally use the present value or future value formula, unsure how to use those formulas in this situation, as I dont have a value for the debt.
any help appreciated. 

If we let $I_k$ and $R_k$ be the interest and principal, respectively, of the $k$th payment, then we know that $I_k + R_k$ = 5000. We can easily calculate (using an amortization table) that $R_k = Pv^{N - k+1}$ where $P$ is the annual payment and $N$ is the term of the loan.
Thus we know that:
$5000 = I_{2n+1} + I_{n+1}= 5000(1 - v^{3n - (2n+1) - 1}) + 5000(1 - v^{3n - (n+1) - 1})$
Or
$1 = 2 - v^{n} - v^{2n}$.
Then just solve the quadratic.
