GP

[Guest]

Encik Mokhtar prepared a sum of RM 20 000 for his son’s monthly expenses at Universiti Sains Malaysia. He deposited RM 500 each month to his son’s account. If Encik Mokhtar invests the remaining money in a fund that offers an interest rate of 1% per month and the interest will be withdrawn from the fund. Find the total amount of the interest earned when the remaining money in the fund to be half of the amount of money in the beginning.

[Guest]

??? If Encik Mohtar invest RM 500 each month and only the interest is withdrawn the amount will never
be "half of the amount of money in the beginning". It will always increase.

[Guest]

I read this a little differently than the previous guest. Encik Mokhtar is NOT investing RM 500 each month. He deposited RM 20 000 in an account earning 1% monthly interest and is sending RM 500 out of that to his son.

The first month the account earns 0.01(20 000)= RM 200. Sending RM 500 to his son leaves 20200- 500= 19700. The second month the account earns 0.01(19700)= RM 197. Sending RM 500 to his son leaves 19897- 500= RM 19397.

If, at the nth month, there are RM [tex]x_n[/tex] in the account, the next month there will be [tex]x_{n+1}= x_n+ 0.01x_n- 500= 1.01x_n- 500[/tex].

Either continue month by month or solve that recursive equation.