1.You just won the Florida lottery, which is currently at $45 million, by picking
the numbers 5, 13, 26, 28, 37, and 48. If you can earn an average yearly rate of
return equal to 6 percent, compound monthly, what would the lump-sum
payment have to equal for you to choose the lump-sum payment rather than a
30 annuity payments of $1.5 million each, with the first payment received
immediately?
2.Five years ago you purchased a house for $200,000. To buy the house, you
borrowed $180,000 at an average yearly rate of 7.2 percent. The mortgage has a
life of 15 years when you bought the house, and it required monthly payments.
Because you have been so successful in your career, you have decided that you
would like to pay off the mortgage. How much do you owe on the mortgage
today (five years after you bought the house)?
唔該幫幫手，真係唔識計><
Quantitative Analysis
2008-12-12 8:21 am
回答 (1)
2008-12-12 10:42 pm
✔ 最佳答案
The unit of the money I suppose to be in US dollars. Therefore I will not include any unit thereafter. I will just play with the figure.1. a lump sum = $45 million = 45'000'000 right?
6% interest rate annually, 0.5% interest rate monthly(just assume), ok?
Compare for 30 years the long run each year took $1.5 million = 1'500'000
45'000'000 1st month interest 0.5% is 225'000, 2nd month is 226'125, 3rd month is 227'255.625.... so on and so on. The calculation is too complicated.
OR
45'000'000 1st year interest 6% is 2'700'000. 2nd year will be 2'862'000... so on and so on
For long term as 30 years, lump sum will be better for interest rate. But this is only simple calculation without other conditions apply to it. So the actual figure is only for reference. The fact is this calculation not appropriate, only work for theory.
Conclusion: lump-sum better money back in term of 30 years
2. $200'000 house 5 years ago
borrow $180'000 5 years ago yearly 7.2% interest rate 15years term
I take that at the time to buy the house cash spent $20'000.
180'000 15years interest is $194'400 (Wow, so much!)
180'000 + 194'400 = 374'400 for total cost in mortgage
monthly installment = 374'400/15years/12months = $2080!! Am I wrong? So much!?!
After paying 2080 for 5 years = 2080x12monthsx5years = 124'800 (include interest 7.2% for 5 years, take note)
On the 6th year, I shall clear all. Total remaining = $120'000 + 1 month interest $1080 = $121'080
Could you figure it out now?
參考: my tree of knowledge
收錄日期: 2021-04-15 21:13:55
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