Question

An engineer planning for her retirement will deposit 10% of her salary each year into a stock found. The initial balance in her stock found (year 0) is $20,000. If her salary this year is $120,000 (end of year 1) and she expects her salary to increase by 5% each year, what will be the future worth of the found after 25 years if it earns 15% per year

Answer 1

$4,202,290.77

Step-by-step explanation:

This can be calculated using the for formula for calculating the future value of growing annuity as follows:

FV = C × {[(1 + r)^n - (1 + g)^n] ÷ (r - g)}

Where;

FV = future value or expected cash flow = ?

C = first year deposit = $120,000 * 10% = $12,000

r = rate of return = 15%, or 0.15

g = growth rate of salary = 5%, or 0.05

n = number of years = 25 years

Substituting all the values into equation (1), we have:

FV = 12,000 × {[(1 + 0.15)^25 - (1 + 0.05)^25] ÷ (0.15 - 0.05)} = $3,543,911.72

FV of initial balance = 20,000 * (1 + r)^n = 20,000 * (1 + 0.15)^25 = $658,379.05

Total FV = FV + FV of initial balance = $3,543,911.72 + $658,379.05 = $4,202,290.77

Therefore, the future worth of the found after 25 years if it earns 15% per year will be $4,202,290.77.