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At the end of this month, Les will start saving $200 a month for retirement through his company's retirement plan. His employer will contribute an additional $.50 for every $1.00 that he saves. If he is employed by this firm for 30 more years and earns an average of 8.25% on his retirement savings, how much will he have in his retirement account 30 years from now?

a. $589,406.19 b. $401,005.25 c. $540,311.67 d. $470,465.70 e. $503,289.01

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Answer:

Amount per month (A) = $200 + $0.50 x $200 = $300

Interest rate (r) = 8.25% = 0.0825

Number of years (n) = 30 years

No of compounding periods in a year (m) = 12

Future value = ?

FV = A(1 + r/m)nm - 1)

               r/m

FV = $300(1 + 0.0825/12)30x12 - 1)

                       0.0825/12

FV = $300(1 + 0.006875)360 - 1)

                   0.006875

FV = $300(1.006875)360 - 1)

                 0.006875

FV = $300 x 1,568.218999

FV = $470,465.70

The correct answer is D

Explanation:

In this case, there is need to apply the formula for future value of an ordinary annuity on the ground that compounding is done monthly. In the formula, monthly deposit (A) is $300, number of years is 30 years and interest rate (r) is divided by 12 because compounding is done on monthly basis. The number of years is also multiplied by the number of times interest is compounded in a year.

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