Please help me with this one question?

1(a) $500 x (1+2%)^{25 x 12}

    = $500 x 1.0230

    = $905.6807920516769 

    \(\approx\)$ 905.68

Max you have found the amount that  500 will grow to in 25 years but this is not the question.

This is like a pension where e500 is paid every month for 25 years.

The question is asking - what would be an equivalent value to have in your hand now if the money is values at 2% pa.

This is the present value of an ordinary anuity

C=500,       i=0.02/12        n=25*12=300       PV unknown

500*((1-(1+0.02/12)^-300)/(0.02/12)) = 117965.0541267359729345119082314998414034840152410787338337814191407       

So the present value of this anuity is   e117,965.05

This means that if you were given e117,965 and put it in the bank at 2%/pa compounded monthly.

or

if you were given e500 every month for 25 years and you put each instalment in the back and it attracted 2%pa compounded monthly interest.  And you left all these instalments in the bank 

THEN

at the end of the 25 years both these scenarios will grow to exactly the same amount of money, namely

117965.05*(1+0.02/12)^300 = e194 410.56

Melody: You got everything right, except if the 500e were deposited in the the Bank @ 2% each and every month for 25 years, that would give you the FV of the annuity, which would amount to $194,410.56e.

SORRY MELODY: DIDN'T READ THE LAST BIT OF YOUR CALCULATION, WHICH IS PERFECTLY CORRECT. SORRY ABOUT THAT!.

That is ok guest :)

The last bit is not really a part of the question.

The question is to find the present value which is e117,965

I just continued on for Max's benefit  - I wanted to help him to understand what the question was about :)

Maybe it helped the poster,  Kcc2468 better understand as well :)

Are you sure that you understand?