Let’s think of it another way so that we can see the impact of compounding on this investment. For simplicity’s sake, we’ll assu
me that Adrian’s rate of return is effectively 5.7% annually (7% - 1.3% fee) and Clemens’s rate is effectively 6.8% annually (7% - 0.2% fee). Each man contributes an additional $100/month into their investment account. Use the compound interest calculator to answer these questions. You can round to the nearest whole dollar and assume the investment compounds annually.
1 answer:
Answer:
annex the questions of the questionnaire because it is incomplete and the answers are made below
Step-by-step explanation:
7. Value of adrian investment in 10 years =
$10000(1+0.057)^10 = $17,408
8. Value of Clemen's investment in 10 years =$10000(1+0.068)^10 = $19,306
9. Additional value of Clemen's investment
over Adrian's investment over 10 years time = $19306-$17408= $1,898
10. Value of Adrain investment in 20 years =$10000(1+0.057)^20= $30,303 Value of Clemen's investment in 20 years =$10000(1+0.068)^20= $37,275
Additional value of Clemen's investment
over Adrian's investment over 20 years time = $37275-$30303= $6,972
11. We can deduce that an actively managed fund charges more brokerage than a passively managed fund.
12. The best reason to choose an actively managed fund is that it has potential
of giving higher returns than index funds (passively managed funds)
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<span>Ayesha's right. There's a good trick for knowing if a number is a multiple of nine called "casting out nines." We just add up the digits, then add up the digits of the sum, and so on. If the result is nine the original number is a multiple of nine. We can stop early if we recognize if a number along the way is or isn't a multiple of nine. The same trick works with multiples of three; we have one if we end with 3, 6 or 9.
So </span>
<span>has a sum of digits 31 whose sum of digits is 4, so this isn't a multiple of nine. It will give a remainder of 4 when divided by 9; let's check.
</span>
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</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1. So we see multiplying by 10 doesn't change the remainder. So
has the same remainder as 
.
When Ayesha reverses the digits she doesn't change the sum of the digits, so she doesn't change the remainder. Since the two numbers have the same remainder, when we subtract them we'll get a number whose remainder is the difference, namely zero. That's why her method works.
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It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:
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So </span>
</span>
</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1. So we see multiplying by 10 doesn't change the remainder. So
When Ayesha reverses the digits she doesn't change the sum of the digits, so she doesn't change the remainder. Since the two numbers have the same remainder, when we subtract them we'll get a number whose remainder is the difference, namely zero. That's why her method works.
<span>
It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:
</span>