Question

Use the gradient method to solve the following problem.

The Diamond Company is planning to purchase a stamping machine in 5 years and plans to save by depositing $20000 at the end of year 1 and will increase the deposits by $5000 each year thereafter. How much will the company have in the account at the end of five (5) years if the interest rate is 4% compounded annually?

Answer 1

I have shown two workings based on assumptions of the timing of deposits.

Formula for Future or Compounded Value = PV*(1+R%)^(N-1)

PV is the Present Value or Annual Deposits

R= Interest %

N = Time period

Time Period	Annual Deposits	Formula	Compounded Value
P1	20000.0	20000*(1+4/100)^(5-1)	23,397.2
P2	5000.0	5000*(1+4/100)^(5-1)	5,849.3
P3	5000.0	5000*(1+4/100)^(4-1)	5,624.3
P4	5000.0	5000*(1+4/100)^(3-1)	5,408.0
P5	5000.0	5000*(1+4/100)^(2-1)	5,200.0
Value at the end of 5 Years			45,478.8
The above calculation is based on the assumption that all the deposits except the Deposit of 20000 in Year 1 are being made at the beginning of the year
Time Period	Annual Deposits	Formula	Compounded Value
P1	20000.0	20000*(1+4/100)^(5-1)	23,397.2
P2	5000.0	5000*(1+4/100)^(4-1)	5,624.3
P3	5000.0	5000*(1+4/100)^(3-1)	5,408.0
P4	5000.0	5000*(1+4/100)^(2-1)	5,200.0
P5	5000.0	No interest	5,000.0
Value at the end of 5 Years			44,629.5
Assumption that all the deposits are being made at the end of the year