2. a couple would like to take a cruise to alaska, 15 months from now. they have $1500 in a savings account. the savings account pays a nominal rate of 1%, compounded monthly. a. if they start investing $110 today for 15 months how much will they have 15 months from today? b. if they start investing $110 a month from now for 15 months how much will they have 15 months from today? c. if they need $3900 for the trip, how much would they need to invest each month, if they make 15 monthly equal investments starting a month from now?

a.- $ 3,529.82  

b.-  $ 3,512.11

c.-  $   132,77

Explanation:

In each case, we must calculate the value of their current savings and the additional investment.

The saving are the same for each scenario so let's calculate that first:

Principal1,500.00

time15 years

rate0.01000

Amount1,741.45

Then we add the funds generated from the investment:

a.- 110 annuity due for 15 month:

C  $ 110

time 15 months

rate0.01

FV$1,788.3651

We add the savings and get a total of:  $ 3,529.82  

b.- 110 ordinary annuity

C  $ 110

time 15 months

rate0.01

FV$1,770.6585

Plus, original savings of 1,741.45 =  3,512.11  

c.-

If they need 3,900 then the fund must cover the difference between these and the savings future value:

3,900 - 1,741.45 = 2,158.55

Now we calculate the PMT, considering the payment are at the beginning:

FV  $ 2,158.55

time  15

rate           0.01

C  $ 132.770

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