Yikes! The teacher that gave you this sure was in a bad mood!

I've reworded your problem this way (same thing):

At annual rate of R%, a loan of 5000 is repaid with N monthly payments of 117.38,

starting one month after the loan is made.

At the same annual rate of R%, N monthly deposits of 113.40 accumulate to 10000

one month after the Nth deposit.

Find the equivalent effective annual rate of interest.

Answer is: 14.4%, 60 months.

To give you an idea of what's involved (and keeping typing to a minimum!):

i = R/12 : u = 117.38 : v = 113.40 : a = 5000 : b = 10000

Using the "loan payment" formula leads to:

(1 + i)^n = u / (u - ai) [1]

Using the "future value of annuity" formula leads to:

(1 + i)^n = 1 + bi / (v(1 + i)) [2]

So:

u / (u - ai) = 1 + bi / (v(1 + i))

Solve for i:

i = (ub - av) / (ab + av)

Substitute back in: i = .012 ; R = .012 * 12 = .144 or 14.4%

The deposit account ends at ~9881.42 after 60th deposit; 9881.42 * 1.012 = ~10000.00