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aliina [53]
3 years ago
6

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. Af

ter 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
Business
1 answer:
Eduardwww [97]3 years ago
6 0

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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Explanation:

Expected return is the return an investor expects from an investment given the investment's historical return or probable rates of return under different scenarios. To determine expected returns based on historical data, an investor simply calculates an average of the investment's historical return percentages and then, uses that average as the expected return for the next investment period.

In the example, the expected return would be:

<em>Expected return </em><em>= (return in a good economy + return in a poor economy)/2</em>

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a).

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replacing;

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