1. A bank offered Peter a loan of $200000 at an interest rate of 12% p.a. compounded monthly. He invests all the money in the stock market immediately after getting the loan. In this loan scheme Peter needs to repay the monthly interest in the first 6 months after getting the loan. When Peter gets the loan, he invests 50%,
30% and 20% of the loan into shares A, B and C at their market prices immediately. 3 months later, Peter sells all the shares st their market prices. The market price of share A has increased by 30%, share B has decreased by 50% and share C has increased by 100%. State whether Peter made a profit or suffered a loss on the whole if the interest paid is the cost of investment. Find his overall profit or loss percent.
2. Express the square root(s) of 32+24i in the form (x+yi), where x and y are real numbers.
mathematics
2012-07-12 9:47 pm
回答 (2)
2012-07-12 10:27 pm
✔ 最佳答案
(1)the amount of the investment of share A = 200000 x 50% = 100000
3 months later, the price of share A = 100000 x (1 + 30%) = 130000
the amount of the investment of share B = 200000 x 30% = 60000
3 months later, the price of share B = 60000 x (1 - 50%) = 30000
the amount of the investment of share C = 200000 x 20% = 40000
3 months later, the price of share C = 40000 x (1 + 100%) = 80000
so he earn 130000 + 30000 + 80000 - 200000 = 40000
on the other hand, the interest of the loan (cost)
= 200000 x (1 + 12%/12)⁶ - 200000 = 12304
therefore, he earn 40000 - 12304 = $27696
and the profit percent = 27696 / 12304 x 100% = 225%
(2)
let x + yi = √(32 + 24i) => (x + yi)² = 32 + 24i
x² - y² + 2xyi = 32 + 24i
therefore, x² - y² = 32 and 2xy = 24
x² - y² = 32 ----------------(i) and y = 12/x -------------------(ii)
subsitite (ii) into (i),
x² - (12/x)² = 32 => x⁴ - 32x² -144 = 0 => (x² - 36)(x² + 4) = 0 => x = ±6
when x = 6, y = 12 / 6 = 2; when x = -6, y = 12 / -6 = -2
thus, √(32 + 24i) = 6 + 2i or -6 - 2i
2012-07-13 15:41:57 補充：
perhaps he just count the interest for the first 3 months
參考: knowledge
2012-07-27 4:28 am
1.
the first 6 months' interest of the loan
= 200000 x (1 + 12%/12)⁶ - 200000 = 12304
the amount Peter really gets (he must repay the interest right after he gets the loan, that means before he invests to the stock market)
= 200000 – 12304 =187696
3 months later, the amount he gets from the stock market is:
187696 x 50% x (1+30%) + 187696 x 30% x (1-50%) + 187696 x 20% x (1+100%)
=225235
So the overall profit percentage should be:
(225235-200000)/200000 x 100%
=12.62%
2012-07-26 20:33:40 補充：
the answer could be wrong
the first 6 months' interest of the loan
= 200000 x (1 + 12%/12)⁶ - 200000 = 12304
the amount Peter really gets (he must repay the interest right after he gets the loan, that means before he invests to the stock market)
= 200000 – 12304 =187696
3 months later, the amount he gets from the stock market is:
187696 x 50% x (1+30%) + 187696 x 30% x (1-50%) + 187696 x 20% x (1+100%)
=225235
So the overall profit percentage should be:
(225235-200000)/200000 x 100%
=12.62%
2012-07-26 20:33:40 補充：
the answer could be wrong
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