PV / FV question

CFA Level I Quant
#1

Hi everyone,

I was able to calculate the answer to this question 2 months ago and now for some reason I cann’t seem to calculate it. It is a PV/FV related question from the Schewer material.

Quesiton:

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 will expect inflation will increase this cost to 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.

My work so far:

I was able to calculate the PV of year 9, 10 and 11.

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

which is accurate according to the “answers” section.

However, I do not know how to calculate the correct PMT answer. The answer according to the book is $1,353.22 but I can’t seem to replicate it.

Sorry for the long post but any help would be fantastic.

#2

Total PV needed = 9806.62

2nd clr TVM

PV=-9806.62

N= 10

Since they say 10 Payments - you need to set calc in Begin Mode (1st cruise is 9 years from now, but they want to make 10 payments)

I/Y=8

FV=0

PMT=?

Ans = 1353.22

1 Like
#3

I am not able to get the answeer mentioned here. As per my calculations annuity payments should be $1,461.48.

#4

cpk123 Have you tried this calculation on a calculator or excel?? Conceptually what you have explained is right, but I can’t get $1,353 as PMT when I used the numbers provided by you.

#5

Change the payment timing to BGN: you should then get $1,353 as PMT.

2nd PMT, 2nd SET until BGN shows in display, 2nd Quit, then do the TVM solve using cpk123’s numbers.

#6

I wrote an article on using timelines in TVM problems that may be of some help here: http://financialexamhelp123.com/time-value-of-money-using-timelines/

Timelines are unquestionably your friends.

#7

In a nutshell,

Since the family wants to make 10 payments and there is only 9 years until the first cruise, you must use the BEGINNING mode on the calculator.

On the HP 10bII+ financial calculator, press the red down arrow, then press the Beg/End button. (the screen should now display “BEG”.)

After, simply input the values cpk123 provided above.

#8

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

The MINUS sign is just the convention for the calculator…

#9

Calculate PV for years 9, 10 and 11 individually, then add together.

Do not forget to divide the inflation rate by the interest rate in the formula.

#10

PV of a 10 payment annuity due is solving for PV at the end of year 9 (beginning of year 10). In this problem, we’re solving for beginning of year 9 value, since the cruise is taken at the beginning of year 9. Is this an error?