first payment is made in 1 year.
second payment is made in 3 years.
third payment is made in 5 years.
fourth payment is made in 7 years.
fifth payment is made in 9 years.
sixth payment is made in 11 years.
since the last payment is made in 11 years, then he has invested each payment for the following number of years.
first payment for 10 years.
second payment for 8 years.
third payment for 6 years.
fourth payment for 4 years.
fifth payment for 2 years.
sixth payment for 0 years.
he will have a total of:
$500 * 1.09^10 plus:
$500 * 1.09^8 plus:
$500 * 1.09^6 plus:
$500 * 1.09^4 plus:
$500 * 1.09^2 plus:
$500 * 1.09^0 equals:
$4818.35
this essentially uses the future value of a present amount formula after you have place the investment in their proper time periods.
you can also use the future value of an annuity formula but it gets tricky because the payments are made every 2 years and the effective interest rate has to be calculated.
looking at it as a future value of a present amount type problem and placing the investments in the proper time periods is the easiest way to solve this one.
the time period investments are as follows:
time period 0 = beginning of year 1
time period 1 = end of year 1 beginning of year 2
time period 2 = end of year 2 beginning of year 3, etc.
here's the list of payments made in their proper time periods:
time period amount
0 0
1 500
2 0
3 500
4 0
5 500
6 0
7 500
8 0
9 500
10 0
11 500
time period 11 is where the future value of the investments are calculated to.
investment in time period 1 is invested for 11 - 1 = 10 time periods.
there is a 1 year interval between time periods.