# excel calculations annual rate with rule 72

## Project Description:

calculating rates of return although appealing to more refined tastes, art as a collectible has not always performed so profitably. during 2003, sotheby’s sold the edgar degas bronze sculpture petite danseuse de quartorze ans at auction for a price of \$10,311,500. unfortunately for the previous owner, he had purchased it in 1999 at a price of \$12,377,500. what was his annual rate of return on this sculpture?
to answer this question, we can use either the fv or the pv formula. both will give the same answer since they are the inverse of each other. we will use the fv formula, that is:
fv = pv (1 + r)t
solving for r, we get:
r = (fv / pv) 1 / t – 1
r = (\$10,311,500 / \$12,377,500)1/4 – 1 = – 4.46%
notice that the interest rate is negative. this occurs when the fv is less than the pv.

my excel calculations:
future value = \$12,377,500.00
present value = \$10,311,500.00
time period = 4

annual rate of return = 4.67% =rate(c123,,-c122,c121)

rule 72
future value = \$12,377,500.00
present value = \$10,311,500.00
time period = 4
annual periods 12
number of periods = 48
rule of 72 150.00%
estimated rate to double 18.00%
using rate 4.57%

fv check -\$12,377,500.00
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