You have 37 years left until retirement and want to retire with $3.4 million. Yo

ID: 2631194 • Letter: Y

Question

You have 37 years left until retirement and want to retire with $3.4 million. Your salary is paid annually, and you will receive $48,000 at the end of the current year. Your salary will increase at 4.1 percent per year, and you can earn a 12.1 percent return on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

Each year salary increases by 4.1 %

=> Each year savings also increases by 4.1 %

Let the saving at the end of year 1 = S

Value of this S at the end of year 37 = S x (1 + 0.121)^36 = S x (1.121)^36

Saving at the end of year 2 = S x (1 + 0.041)

Value at the end of year 37 = S x (1.041) x (1.121)^35

Similarily,

Saving at the end of year 3 = S x (1 + 0.041)^2

Value at the end of year 37 = S x (1.041)^2 x (1.121)^34

...........

Saving at the end of year 37 = S x (1 + 0.041)^36

Value at the end of year 37 = S x (1.041)^36 x (1.121)^0

Value of total savings = 3400000

=> S x (1.121)^36 + S x (1.041) x (1.121)^35 + S x (1.041)^2 x (1.121)^34 + ........ + S x (1.041)^36 x (1.121)^0 = 3400000

=> S x (1.121)^0 x (1.041)^36 x ((1.121 / 1.041)^37 - 1) / ((1.121 / 1.041) - 1)

=> S x 800.41 = 3400000

=> S = $ 4247.82

% saving = 4247.82 x 100 / 48000 = 8.85 % savings need to be done each year

Navigate

You have 36 years left until retirement and want to retire with $4.9 million. Yo

You have 38 years left until retirement and want to retire with $4. 2 million. Y

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.

You have 37 years left until retirement and want to retire with $3.4 million. Yo

Question

Explanation / Answer

Related Questions

Navigate