First off this question is a little ambiguous as it does not state the type of interest rate, are we working with 6% per year nominal compounding monthly or 6% per year effective. I will assume that we are working with 6% per year effective, if this is the wrong assumption please replace the interest rate with i = 0.06/12 = 0.005 (i.e half a per cent). I will also assume that the first payment is made at time 0 (i.e. payments are made in advance)Two people want to take a trip to Nepal in two years. They set up a sinking fund at 6% interest. What will the monthly deposit be if they want the funds value to be 20,000 in two years. The account is an ordinary annuity.
The way i will approach this problem is to first find the present value of the 20000 and then equate that to the present value of the annuity. I will work in periods of one month.
Let i be the effective rate of interest per month: i = (1.06)^(1/12) - 1 = 0.04867551
Hence the present value of the 20000 is = 20000(1+i)^(-24) = 17799.9288
You should be aware of the formula for the present value of an annuity payable in advance, that is: Installment * (1 - (1+i)^(-n)) / (i/(1+i)) where n is the number of installments.
now equate the present value of the annuity with the present value of the 20000 and solve for the installment:
17799.9288 = Installment * (1 - (1+i)^(-24)) / (i/(1+i)) = Installment * 22.70937022
=> Installment = 783.8142856
I hope this is helpful to you, please let me know if I should change my assumptions and revise the post accordingly.