Question

10. Paimin Bin Paijo a 30-year-old Bachelor of Mechanical Engineering, next year his salary will be up to $80,000. Paimin hopes his salary will always rise every year at a rate of a steady increase of 6% per year until he retires at age 60. If Paimin saves money 10% of his salary each year and invests his savings at an interest rate of 8%, How much money will Paimin have when he retires at age 60?

(Please write down the answer on the paper step bye step)

Answer 1

Data given:

• Salary at 30 year age (P) = $ 80,000
• Increase in salary per year (r) = 6 %
• Savings every year (S) = 10 %
• Interest on savings (i) = 8 %

Calculation:

• The salary after Nth year will be given by equation = P [1 + r/100]^N
• Savings every year = {P[1 + r/100]^N}/10}
• Savings after Nth year = {P[1 + r/100]^N}/10 × [1 + i/100]^N
  • = P/10 × [1 + r/100]^N × [1 + r/100]^N
• Hence his savings when he reaches 60 years age, ie after 30 years will be given by: 80,000/10 × [1 + 6/100]³⁰ × [1 + 8/100]³⁰
  • = 8,000 × [106/100]³⁰ × [108/100]³⁰
  • = 8,000 × [(106×108) ÷ (100×100)]³⁰
  • = 8,000 × (11,448/10,000)³⁰
  • = 8,000 × (1.1448)³⁰
  • = 8,000 × 57.7948
  • = $ 462358

​​​​​​​Hence the Paimin will have $ 462358 when he retires at 60.