Question

ebhat is going on vacation in exactly 4 months. His options for paying for it are
1. pay $4000.00 up front (today)
2. make 4 payments of $X at the end of each month for the next 4 months.
3. Pay $1000.00 today and pay 3 * $X on the day he leaves (t = 4 months).
a) If X = 1100.00 what monthly compounded interest rate r(12) makes options 1 and 2 equally expensive?
b) Use your answer to a) to find the cost (present value) of option 3).
c) True or False: Option 3 is always cheaper than Option 2 no matter what the interest rate is.

Answer 1

$1100×4=4400$

$P(1+r)^n$

$4000(1+r)^4=4400$

$(1+r)^4=1.1$

$1+r=1.02411$

$r=0.02411=2.411\%$

The compound intrests that makes a more expensive should be >2.411%

b.The future cost of this amount is

$1000+(3×1100)=4300$

Pv of a future sum =

$$Fv\over(1+r)^n$$

$$4300\over(1+{2.411\over100})^4$$

$$=3909.0923$$

c .Its true that option 3 is cheaper than option 2