please show all work & make sure its legible and organized so i can understand w

Question

please show all work & make sure its legible and organized so i can understand what im looking at. Assume that you have $6,000 in the bank, and that you are going to receive $1,500 three times a year until the day of your retirement (20 years from now). You also need to pay $900 every year for 6 more years (Student loans). You know from your retirement that you will receive deposits of $12,000 annually for 20 years after you retire. What is the present value of all of these cash flows if the annual interest rate is 12%?

Explanation / Answer

i) Existing bank balance = 6000

ii) 1500 three times a year for 20 years

Assuming you receive 1500 every 4 months

so, totally n = 20*3 = 60 payments

r = 12%/3 = 4%

PMT = 1500

PV = PMT*(1-(1+r)-n) / r = 1500*(1-(1+4%)-60)/4% = 33935.23

iii)

student loan of 900 for 6 years

PV = PMT*(1-(1+r)-n) / r = 900*(1-(1+12%)-6)/12% = 3700.27

iv)

after retirment 12000 every year for 20 years

value at reitrment = PMT*(1-(1+r)-n) / r = 12000*(1-(1+12%)-20)/12% = 89633.32

PV of that amount = 89633.32*(1+12%)-20 = 9292.00

Total value = 6000 + 33935.23 - 3700.27 + 9292.00 = 45526.97

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