Answer:
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).
