Question

You bought 500 forever stamps just before the price went up in January of 2014 at $0.46/stamp, a $0.03 savings per stamp. If you could have paid off a credit card charging 12% per year instead of investing in stamps, how fast must you use the stamps to breakeven? Assume the $0.49 price never changes before you run out of stamps. (Hint use 12% / year as your effective interest rate per year)

a. 3 months

b 6 months

c 10 months

d 12 months

e 36 months

Answer 1

You bought 500 forever stamps just before the price went up in January of 2014 at $0.46/stamp, a $0.03 savings per stamp.

The price of stamp after increase is $0.49/stamp

Suppose you have paid off a credit card charging 12% per year

You must use the stamps to breakeven is x (assumed)

Now we can use following formula to calculate x

PV = FV / (1+i) ^n

Where,

PV is the present value or price of stamp = $0.46/stamp

FV is the future value or price of stamp after price increase = $0.49/stamp

i is the interest rate = 12% per year

n is time period = x

Therefore,

$0.46 = $0.49/ (1+12%) ^x

Or (1+12%) ^x = $0.49/ $0.46 = 1.06522

Taking natural log (ln) from both sides

Ln (1+12%) ^x = ln 1.06522

Or x * ln (1+12%) = ln (1.06522)

Or n = ln (1.06522) / ln (1.12)  

Or n = 0.0632 /0.1133

Or n = 0.56 years or 6.67 months

6.67 months are required for break-even; therefore you must use within 6 months for break-even

Therefore best option is option b. 6 months