You want to be a millionaire when you retire in 40 years. a. How much do you have to save each month if you can earn an annual return of 11.6 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.) b. How much do you have to save each month if you wait 10 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.) c. How much do you have to save each month if you wait 20 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

The answers are:

a. 1866.79

b. 2489.05

c. 3733.57

Explanation:

a. Let us begin by calculating the total amount to be saved each year.

Let the total amount to be saved each year be "m"

annual return = 11.6% of m = 11.6 ÷ 100 = 0.116 of m

Therefore to be a millionaire in 40 years, the total amount saved for the year + the annual return on that amount when multiplied by 40 will yield 1 million. It is represented thus:

(0.116m + m) × 40 = 1,000,000

= (1.116m) × 40 = 1,000,000

44.64m = 1,000,000

∴ m = 1,000,000 ÷ 44.64 = 22401.433691756

therefore amount to be saved for a year = 22401.433691756

to calculate amount to be saved each month we divide this amount by 12, because 12 calendar months make one year. Hence;

amount to be saved each month = 22401.433691756 ÷ 12 = 1866.79 (to 2 decimal places).

b. If you wait 10 years, then you have only 30 years left to save

since the annual return remains the same,

(0.116m + m) × 30 = 1,000,000

(1.116m) × 30 = 1,000,000

33.48m = 1,000,000

∴ m = 1,000,000 ÷ 33.48 = 29868.578255675 (amount to be saved for a year)

Therefore amount to be saved per month = 29868.578255675 ÷ 12 = 2489.05 ( to 2 decimal places)

c. If you wait 20 years before saving, you hve 20 years more to save.

Since the annual return remains the same;

(1.116m) × 20 = 1,000,000

22.32m = 1,000,000

m = 1,000,000 ÷ 22.32 = 44802.867383512 (yearly amount to be saved)

Therefore amount to be saved per month = 44802.867383512 ÷ 12 = 3733.57 ( to 2 decimal places).

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