Question

PLEASE WRITE DOWN COMPOUND INTEREST FACTORS

6- Suppose you are 25 years old and just got hired by a company. Your salary next year will be $60,000. Also, you should expect that your salary will increase at a steady rate of 4.5% per year until your retirement at age 65, If you save 10% of your salary each year and invest these savings at an interest rate of 6%, how much will you have saved at your retirement?

Answer 1

This question is related with geometric gradient factor. By using the compound interest factor and formula first we have to calculate the PW of the gradient series cash flow and then by using the single payment future worth factor calculate the FV of the PW of the saving.

Salary in the 26 k year = $ 60,000 Expected to increase by 4.5 % until the retirement Retirement = 65 years Life = 40 years. 10 % of the salary to be saved every year Annual savings = 10 % of 60,000 = 6,000 Increases by 4.5 % every year(Gradient) Rate of interest = 6% calculate PV of the savings. PV = 6000(p/A_1, 4.5 %, 6 %, 40) PV = 6000[1 - (1 + .045)^40 (1 + .06)^-40/-06 - -0.45] pv = 6000(28.9680) PV = 173,808 Savings of the investment at the age of retirement will be = $ 173,808(F/p, 6 %, 40) FV = $ 173,808(10.2857) = $ 1.787,737 Geometric gradient Formula Factor = (p/A_1, g, c, N) Formula = P = A_1[1 - (1 + g)^N (1 + c)^-N/1 - 8] or p = A_1 (N/1 + i) of I = 8 Future value at the retirement is $ 1,787,737