Question

An equipment is bought at $100,000 and the depreciation period is assumed to be 4 years. The salvage value is estimated to be $20,000. What is the depreciation expense each year using the sum of the year’s digits approach? Show your calculations for full credit.

	Depreciation	Book value
Year 1
Year 2
Year 3
Year 4

2.b

Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has $10,000 in it and pays a 5% interest rate. Assume annual compounding.

1. How much money would be in the account if you left the money there until your 25th birthday?

2. What if you left the money until your 65th birthday?

3. How much money did your grandfather originally put in the account?

Answer 1

a]

Sum of year's digits = 1 + 2 + 3 + 4 = 10

Depreciation in Year 1 = (4 / 10) of depreciable value

Depreciation in Year 2 = (3 / 10) of depreciable value

Depreciation in Year 3 = (2 / 10) of depreciable value

Depreciation in Year 4 = (1 / 10) of depreciable value

Depreciable value = cost - salvage value = $100,000 - $20,000 = $80,000

1 Year Depreciation Book Value 32,000 68,000 24,000 44,000 16,000 28,000 8,000 20,000

C А 1 Year 2 1 32 43 54 в Depreciation =(4/10) *80000 = (3/10) *80000 =(2/10) *80000 =(1/10)*80000 Book Value =100000-B2 =C2-B3 =C3-B4 =C4-B5

b]

future value = present value * (1 + rate of return)^{number of years}

Money in account on 25th birthday = $10,000 * (1 + 5%)⁷ = $14,071 (there are 7 years between 18th and 25th year)

Money in account on 65th birthday = $10,000 * (1 + 5%)⁴⁷ = $99,059.71 (there are 47 years between 18th and 65th year)

Money in account on 18th birthday = Money in account on day you were born * (1 + 5%)¹⁸

$10,000 = Money in account on day you were born * (1 + 5%)¹⁸

Money in account on day you were born =  $10,000 / (1 + 5%)¹⁸ = $4,155.21