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Three colleagues - Alice, Bob and Carol - are planning for their retirement. They are currently 25 years old, and each aim to save $500000 by the time they retire at 65.
Alice decides to invest $60000 in a savings account offering an interest rate of 6% per annum, compounded annually.
Find the value of Alice's savings after 40 years.
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Determine Alice's age when her investment reaches the target.
Bob invests $46000 in a savings account offering an interest rate of 6% per annum with k compounding periods per year.
Find the minimum value of k such that Bob's savings reach the target within 40 years.
Carol decides not to put her money in a investment account, and instead makes yearly deposits into an account that pays no interest. Each year, she deposits 5% of her salary into this account. At age 25, her salary is $100000 per year, and each year she gets a raise of q%, where q is set to one decimal place.
Determine the age at which Carol will reach her goal if q=8.
Find the minimum value of q such that Carol reaches her savings target by the time she retires.
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