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Anne plans to save $40 a week, starting next week, for ten years and earn a rate of return of 4.6 percent, compounded weekly. After the ten years, she will discontinue saving and invest her account at 6.5 percent, compounded annually. How long from now will it be before she has accumulated a total of $50,000?A) 10.32 yearsB) 21.14 yearsC) 15.08 yearsD) 11.14 yearsE) 20.32 years

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facundobuzzetti

Answer:

The correct answer is B.

Explanation:

Giving the following information:

Anne plans to save $40 a week, starting next week, for ten years and earn a rate of return of 4.6 percent, compounded weekly. After the ten years, she will discontinue saving and invest her account at 6.5 percent, compounded annually.

First, we calculate the final value of the first ten years:

Effective rate= 0.046/52= 0.000885

n=52*10= 520

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {40*[(1.000885^520)-1]}/0.000885= 26,398.57

Now, we can calculate the number of years.

n=[ln(FV/PV)]/ln(1+i)

n= [ln(50,000/26,398.57)]/ln(1+0.065)

n= 10.14 years

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