What equal contribution must they make today and every year until their first cruise (ten contributions) in order to have saved enough at that time for all 3 cruises?
A couple plan to take 3 criuses,1 each year. will take 1st cruise 9years from today. 2nd cruise 1year after that,then 3rd cruise 11 years from today.
The type of cruise they will take currently costs $5000 but they expect inflation will increase this cost by 3.5% per year on average. They will contribute to an account to save for these cruises that will earn 8% per year. They pay for cruises when taken.
Hope I can get some help with this maths finance problem.
The best way to approach this problem is to use a spreadsheet application such as eXcel that will allow you to keep track of the data on a year-by-year basis.
Based on the way the problem is described, it appears that there will be a total of 12 years to consider. The first cruise will be taken in Year 10, with the following cruises taken in Year 11 and Year 12 respectively. However, the family must have the money for all three cruises by the end of Year 10. Thus, the family will have to pay for all three cruises after contributing a set some each of the first 10 years.
Start by calculating what the cruises will cause in Year 10, Year 11 and Year 12. The cruise is estimated to cost $5,000 today, but will increase, due to inflation, by 3.5% every year. Thus, we will calculate the total price of the first cruise (in year 10, but 9 years from now)by using the following formula:
Amount at year x = 5000(1 + 0.35)^9
(calculate cruise #2 using 10 and cruise #3 using 11)
Price of first cruise = $6814.49
Price of second cruise = $7,052.99
Price of third cruise = $7,299.85
Thus, the total amount that the family needs to have by year 10 is $21,167.33.
At this point, there is an issue with the problem. Based on the way it is described, it does not appear that any interest rate is taken into account for the savings and it does not factor into the equation the present value of money. Therefore, the assumptions are that the present value of money is equal to the future value of money (i.e. $10 today is worth the same as $10 in ten years) and the family is not investing the money into any account that would provide interest. Therefore, all we have to do is take the amount of money that they will need ($21,167.33) and divide it by 10 contributions to get $2,116.73. This is the amount that the family will need to contribute to the cruise fund each of the first ten years in order to be able to afford the cruises.
As stated above, this is flawed due to the lack of consideration of the time value of money and any ability to accrue interest on the savings over time.
To calculate the information on your own, you will need to find an annuity chart. The link below shows you exactly how to do it.
Additional information provided for question:
What if the family is receiving 8% annual interest rate on the amount they save?
There are calculations that can be used to figure this out. The easiest way, however, is to use an online financial calculator such as the one included in the site listed below:
If you need to have $21,167.33 by the 10th year and you have it in an account earning 8% interest, you will need to save $1,461.17 per year.