# Math Help - Geometric Series Help (time payments)

1. ## Geometric Series Help (time payments)

Hello, can someone help me with this.

A man is to receive six payments of $500 each, the first payment in a year's time and subsequent payments at two-yearly intervals. He invests each payment at 9 per cent per annum. How much will he have immediately after the last payment is made. Answer is$4818

and

A firm is established with new equipment and creates a fund to provide for the replacement of the equipment after 6 years at an estimated cost of $20 000. How much should be paid into the fund anually if interest at 11 % can be obtained. Answer is$2528

Can someone help me derive the equations...? I know how to do the rest. Thanks

2. Originally Posted by noobonastick
Hello, can someone help me with this.

A man is to receive six payments of $500 each, the first payment in a year's time and subsequent payments at two-yearly intervals. He invests each payment at 9 per cent per annum. How much will he have immediately after the last payment is made. Answer is$4818
The last paymet is worth $\500$, the one befor that $\500(1+9/100)^2$ (that is the principle plus two years of interest compounded annually, the one before that $\500(1+9.100)^4$, .. So the total is:

$
500(1+1.09^2+1.09^4+1.09^6+1.09^8+1.09^{10})=500 \times\frac{1-(1.09^2)^{6}}{1-1.09^2}
$
dollars

CB

3. Originally Posted by noobonastick
A firm is established with new equipment and creates a fund to provide for the replacement of the equipment after 6 years at an estimated cost of $20 000. How much should be paid into the fund anually if interest at 11 % can be obtained. Answer is$2528
Solve for R in the following
$
20,000 = R\frac{{\left( {1.11} \right)^6 - 1}}
{{.11}}
$