Sept 2002 Q11

A loan of £10,000 was granted on 1 April 1994. The loan is repayable by an annuity payable monthly in arrears for 15 years. The amount of the monthly repayment increases by £10 after 5 years and by a further £10 after 10 years,
and was calculated on the basis of a nominal rate of interest of 8% per annum convertible quarterly.(i) Calculate the initial amount of monthly repayment.

i want to working in year
i=(1+0.08/4)^4 -1 = 0.08243216

10000= 12*X*[1-(1+I)^-5]/i(12) +X* v^5*10*12*[1-(1+I)^-5]/i(12)
+ X*v^10*10*12*[1-(1+I)^-5]/i(12)
is my equation correct? after solving equation i dont get correct ans.
what is mistake?

 

I don't think that formula is correct.. My suggestion is to rewrite the formula for this:

Loan =

Annuity of X for 15 years
+ Annuity of 120 (or 10x12) for 10 years, deferred for 5 years (v^5)
+ Annuity of 120 (or 10x12) for 5 years, deferred for 10 years (v^10)

Having the variable you're trying to solve for (X) in the equation three times makes it more complicated when based on my reading of the question you only need to have it in once, as above.

Give it another go and feel free to correct my understanding of the question.. if you still have problems post the answer and I'll do the workings to get there.