Question
Person A deposits $5000 to his account. He is going to make a withdrawal twice, first one after 6 months and the second one at the end of the year (after 12 months). After these two withdrawals his account will be empty and the amount of withdrawal is the same both time. Calculate the withdrawal amount when the interest rate is 2.5% per annum.
My attempt
$k=5000, i=0.025, t=\dfrac{1}{2}$
Interest in the first six months is $r=kit=5000*0.025*\dfrac{1}{2}=\dfrac{125}{2}=62.5$
$K_1=5000+r=5062.5$
By generalising the interest I get that $f(x)=x*0.025*\dfrac{1}{2}=\dfrac{x}{80}$
Now, $K_2$, the amount of money interest included for the latter half of the year, is the same as $x$, the amount of money to withdraw to empty the account. The amount of money left after the first withdrawal is $K_1-x$. This leads me to the following equation:
$x=f(K_1-x)+K_1-x$
Solving for $x$ gives $x=\dfrac{81K_1}{161}$
Substituting and evaluating gives $x=\dfrac{81*5062.5}{161}\approx2546.97$
The answer I got is almost correct, but not quite and I'm wondering if my approach is correct.
Best Answer
Answer should be 2546.58.
If you see the same answer in your answer sheet, go ahead...
The mistake you are making is, after the first withdrawal, you are taking principal as $\left(5062.5 - a\right)$ assuming $a$ to be the amount he withdraws.
But for simple interest, it should be $5000-a$. Withdrawal is from principal and only principal left from initial deposit is considered for interest. And you are done.