"The Parks plan to take three cruises, one each year. They will take their first cruise 9 years from today, the second cruise one year after that, and the third cruise 11 years from today. The type of cruise they will take currently costs $5,000, 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. What equal contributions must they make today and every year until their first cruise (ten contributions) in order to have saved enough at that time for all three cruises? They pay for cruises when taken."
"Our suggested solution method is:"
PV (first cruise) = 5000 x [( 1.035 ^9) / (1.08 ^9)] = 3,408.94 PV (second cruise) = 5000 x [( 1.035 ^10) / (1.08 ^10)] = 3,266.90 PV (third cruise) = 5000 x [(1.035^11 / 1.08^ 11)] = 3,130.78 Total PV = Sum of above 3 = 9806.62
"PV of all three = 3,408.94 + 3,266.90 + 3,130.78 = $9,806.62. This is the amount needed in the account today, so it’s the PV of a 10-payment annuity due. Solve for payment at 8% = $1,353.22."
On Calculator:
N= 10 I/Y=8 FV=0 PMT=? Ans = 1353.22
PV of a 10 payment annuity due is solving for PV at the end of year 9 (beginning of year 10). In this problem, if I did not misunderstand, we want to solve for the value at the beginning of year 9, since the cruise is taken at the beginning of year 9 (9 years from today).
The given solution, on the BA II Plus: BGN Mode --> annuity due problem N = 10 I/Y = 8% PV = $9,806.62 PMT = ?
Solving for PMT here is solving for the value at the end of year 9. Is this solution incorrect since the cruise is taken 9 years from today (beginning of year 9)?
Am I missing something or is there an error in this question?
Thanks.
