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Assume that you are 30 years old today,and that you are planning on retirement at age 65.Your current salary is $45,000 and you expect your salary to increase at a rate of 5% per year as long as you work.To save for your retirement,you plan on making annual contributions to a retirement account.Your first contribution will be made on your 31st birthday and will be 8% of this year's salary.Likewise,you expect to deposit 8% of your salary each year until you reach age 65.Assume that the rate of interest is 7%.
-The present value (PV)(at age 30)of your retirement savings is closest to:
A)$87,000
B)$108,000
C)$46,600
D)$75,230

Question

Quizplus · Accepted Answer

The correct answer is A because the present value of the retirement savings is closest to $87,000. This can be calculated using the formula for the present value of an annuity, which is:PV = PMT * [1 - (1 + r)^-n] / rwhere:PMT is the annual contributionr is the interest raten is the number of yearsIn this case, the annual contribution is 8% of the salary, which is $45,000 * 0.08 = $3,600. The interest rate is 7%, and the number of years is 35 (from age 31 to age 65). Plugging these values into the formula, we get:PV = $3,600 * [1 - (1 + 0.07)^-35] / 0.07 = $86,947.68This is closest to $87,000, which is choice A.

Use the Information for the Question(s)below