Question

Please write down all the steps.

What is the future value 10 years from now of $1,800 invested today at a periodic interest rate of 10% compounded annually?

Assuming a MARR of 14%, how much should you save each month to accumulate $1,000,000 over the next 25 years?

A construction company purchases a truck for $125,000, and will sell it for $20,000 at the end of five years. The annual operating cost of the truck is $40,000. What is the equivalent annual cost of the truck, if the company uses a MARR of 12%?

Answer 1

Answer 1
We can use the Future value of lumsum formula to calculate Future value of amount invested today
Future Value of lumsum = P x (1+r)^n
Future value of lumsum = ?
P = amount invested today = $1800
r = interest rate per annum = 10%
n = number of years = 10
Future Value of lumsum = 1800 x (1+0.10)^10
Future Value = $4,668.74
Answer 2
We can use the Future value of annuity formula to calculate the monthly savings.
Future value of annuity = P x {[(1+r)^n -1]/r}
Future value of annuity = amount accumulated over 25 years = $10,00,000
P = monthly savings = ?
r = interest rate per month = 14%/12 = 0.011667
n = number of months savings = 25 years x 12 = 300
1000000 = P x {[(1+0.011667)^300 -1]/0.011667}
1000000 = P x 2695.826
P = 370.94
You should save $370.94 per month to accumulate $1,000,000 over the next 25 years
Answer 3
Calculation of EAC i.e. Equivalent annual cost of the truck
EAC = Operating cost per year + [(Purchase cost of truck - Present value of it's sale value) / Annuity Factor @ 12%]
Present value of Truck's sale value = Sale value x Discount factor of 5th year @ 12%
Present value of Truck's sale value = $20000 x (1+0.12)^-5 = $11,348.54
Annuity factor = [1 - (1+r)^-n]/r where r = discount rate and n = number of years
Annuity Factor @ 12% = [1 - (1+0.12)^-5]/0.12 = 3.604776
EAC = $40000 + [($125000 - $11348.54) / 3.604776]
EAC = $40000 + $31528.02
EAC = $71,528.02
The equivalent annual cost of the truck = $71,528.02