Question

Exercise 3 if you invest $4000 each year for 40% years, how much will you have at the end of 40 years assuming a 9% annual return?

Exercise 4 if you want to withdraw $35000 each year for 30 years, how much would you need to have saved today to fund these withdrawals? (Assume 7% annual return)

Exercise 5 if you purchase a machine and borrow $30000, what will your approximate monthly payment be if you pay back the loan over 5 years. Assume a 10% interest rate.

Exercise 6 You are considering purchasing a new machine for $32000 that will save $6000 per year for 8 years. If cost of capital is 12%, what is the net present value (NPV) of buying the new machine?

Answer 1

Part 3

Future value = annual payment * future value annuity

= 4000*(((1.09^40)-1)/9%) = $1351530

Future value annuity =( (1+r)^n -1)/r

R = 9%

N= 40

Part 4

Present value = annual withdrawal * present value of annuity

= 35000*((1-(1.07^-35))/7%)

= $453168.53

= $453169

Present value of annuity = ((1-((1+r)^-n))/r)

R = 7%

N= 35

Part 5

Monthly payment = PV/present value of annuity

=30000/(((1-((1+(10%/12))^-60))/(10%/12))) = $637.41 = $637

Present value of annuity = ((1-((1+r)^-n))/r)

R= 10%/12

N = 5*12 = 60

Part 6

NPV = present value of cash inflows – present value of cash outflows

= -32000+(8000/(1.12))+ (8000/(1.12^2))+ (8000/(1.12^3))+ (8000/(1.12^4))+ (8000/(1.12^5))+ (8000/(1.12^6))+ (8000/(1.12^7))+ (8000/(1.12^8)) = $7741.12 = $7741

PV = C/(1+r^n)

R = 12%