Question

The original price of a car is entered into spreadsheet cell A1 and the annual depreciation amount in cell B1.

a. Write the spreadsheet formula to determine the number of years it will take for the car to totally depreciate.
b. The spreadsheet user is instructed to enter a car value in cell D1. Write the spreadsheet formula to compute how long it will take for the car to depreciate to that value.
c. The spreadsheet user is instructed to enter a percent into cell E1. Write the spreadsheet formula to compute the length of time it will take for the car to decrease by that percent.

Answer 1

A1 / B1 ;

(D1 - A1) / B1 ;

(A1 - E1*A1) / B1

Explanation:

A1 = original price of car

B1 = annual Depreciation amount

Number of years it will take for the car to depreciate totally :

Using the straight line Depreciation relation :

y = mx + c

c = intercept = initial or original value of car

m = annual Depreciation amount

x = number of years

y = value after x years

For total Depreciation, final value, y = 0

0 = mx + c

mx = - c

x = - c / m

Hence, x = A1 / B1

B.)

D1 = car value

Length it will take for car to depreciate to value in D1 :

y = mx + c

y = D1; m = B1 ; c = A1

D1 = B1x + A1

B1x = D1 - A1

x = (D1 - A1) / B1

C.)

E1 = decrease percentage

Time it takes for car to decrease by percentage in E1

y = E1 * A1

E1 * A1 = B1x + A1

(A1 - E1*A1) = B1x

x = (A1 - E1*A1) / B1