Question

A care price is $12,000 & its market value after 7-years is $5,000. In addition its
price is ascending by 4% yearly, estimate the following:
a. Depreciation rate in the first five years of its life.
b. Total depreciation in that period also.
c. The inflation rate.

Answer 1

a) $S^*=(((((((S*i)-P)*i-P)*i-P)*i-P)*i-P)*i-P)*i-P$

$S^*=S*i^7-P*\frac{i^7-1}{i-1}$

$P=(S*i^7-S^*)*\frac{i-1}{i^7-1}$

P-annual payments

S-the care price

S^*-the market value after 7-years

$i=1+0.04=1.04$

$P=12,000*1.04^7-5,000)*\frac{1.04-1}{1.04^7-1}=1,366.27$

$D=\frac{P}{S}*100\%$

D-Depreciation rate

$D=\frac{1,366.27}{12,000}*100\%=11.39\%$

b) $1,366.27*7=9563.89$

c) The inflation rate is 4%