作业帮英文数学题(2)Four years ago,Emily secured a bank loan for $200,00
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英文数学题(2)
Four years ago,Emily secured a bank loan for $200,000 for the purchase of a house.The term of the mortgage is 30 years ,with an interest rate of 9.5%/year compounded monthly.Because the interest rate for a conventional 30-year mortgage has now dropped to 6.75%/yearly compounded monthly,Emaily is thinking of refinancing her property.
a.what is emilys current monthly mortgage payment?
b.What is emilys current outstanding principle?
c.If Emily decides to refinance her property by securing a 30 year home mortgage loan in the amount of the current outstanding principle at the prevailing interest rate of 6.75%/yearly compounded monthly,what will be her monthly mortgage payment?
d.How much less would Emily monthly mortgage payment be if she refinances?
Four years ago,Emily secured a bank loan for $200,000 for the purchase of a house.The term of the mortgage is 30 years ,with an interest rate of 9.5%/year compounded monthly.Because the interest rate for a conventional 30-year mortgage has now dropped to 6.75%/yearly compounded monthly,Emaily is thinking of refinancing her property.
a.what is emilys current monthly mortgage payment?
b.What is emilys current outstanding principle?
c.If Emily decides to refinance her property by securing a 30 year home mortgage loan in the amount of the current outstanding principle at the prevailing interest rate of 6.75%/yearly compounded monthly,what will be her monthly mortgage payment?
d.How much less would Emily monthly mortgage payment be if she refinances?
这是哪里的题啊,不像数学啊.金融里的吗?
先讲一下复利公式：
本金为S,年利息为r,月复利,即一年记息12次,1年末的钱变成S(1+r/12)^12.{表示12次方}
钱变多了,这说明钱有时间价值,现在的S元,相当于一年后的S(1+r/12)^12元.
而一年后的T元,现在只值T/{(1+r/12)^12}元.
a.
对于公平的货款,应该是这样的：
每个月还的钱的未来价值加起来 = 最开始的货款在未来的价值
设Emily每月还钱为P.
第一个月还的钱在货款终止时在银行里待了359个月,此时价值为P(1+9.5%/12)^359.
第二个月还的钱在货款终止时在银行里待了358个月,此时价值为P(1+9.5%/12)^358.
.
第359个月还的钱在货款终止时在银行里待了1个月,此时价值为P(1+9.5%/12)
第360个月还的钱就在货款终止时,此时价值为就为P.
总价值为:P(1+9.5%/12)^359+P(1+9.5%/12)^358+...+P(1+9.5%/12)^1+P {这是等比数列,有公式的}.
而最初借的钱200000在360个月后,价值为200000*(1+9.5%/12)^360.
30年后借钱的价值和还钱的价值应该是相等的.所以
200000*(1+9.5%/12)^360=P(1+9.5%/12)^359+P(1+9.5%/12)^358+...+P(1+9.5%/12)^1+P
解得:P=1681.
b.
最佳策略当然是重新借钱啊,因为利息低了,不用还那么多利息了.
c.
4年后即48个月后,我们要计算现在还有多少钱要还.
此时我们还的48个月的钱,每月还P,在48个月后的价值为:
P(1+9.5%/12)^47+P(1+9.5%/12)^46+...+P(1+9.5%/12)^1+P=97695
而此时原贷款200000的价值为200000*(1+9.5%/12)^48=292019
此时还要还货款的值为292019-97695=194324.
设新利息下每月还钱为Q,则按类似的方式得:
新货款30年(360个月)后的总价值为:
Q(1+6.75%/12)^359+Q(1+6.75%/12)^358+...+Q(1+6.75%/12)^1+Q
而新借的钱194324在360个月后,价值为194324*(1+6.75%/12)^360.
以上两者应相等:
Q(1+6.75%/12)^359+Q(1+6.75%/12)^358+...+Q(1+6.75%/12)^1+Q
=194324*(1+6.75%/12)^360.
解得 Q=1260.
d.
原来应交的钱为:P*360=605160
新方案应交的钱为:P*48+Q*360=534288
所以少交了很多钱-_- 605160-534288=70872
你明白了吗?.
先讲一下复利公式：
本金为S,年利息为r,月复利,即一年记息12次,1年末的钱变成S(1+r/12)^12.{表示12次方}
钱变多了,这说明钱有时间价值,现在的S元,相当于一年后的S(1+r/12)^12元.
而一年后的T元,现在只值T/{(1+r/12)^12}元.
a.
对于公平的货款,应该是这样的：
每个月还的钱的未来价值加起来 = 最开始的货款在未来的价值
设Emily每月还钱为P.
第一个月还的钱在货款终止时在银行里待了359个月,此时价值为P(1+9.5%/12)^359.
第二个月还的钱在货款终止时在银行里待了358个月,此时价值为P(1+9.5%/12)^358.
.
第359个月还的钱在货款终止时在银行里待了1个月,此时价值为P(1+9.5%/12)
第360个月还的钱就在货款终止时,此时价值为就为P.
总价值为:P(1+9.5%/12)^359+P(1+9.5%/12)^358+...+P(1+9.5%/12)^1+P {这是等比数列,有公式的}.
而最初借的钱200000在360个月后,价值为200000*(1+9.5%/12)^360.
30年后借钱的价值和还钱的价值应该是相等的.所以
200000*(1+9.5%/12)^360=P(1+9.5%/12)^359+P(1+9.5%/12)^358+...+P(1+9.5%/12)^1+P
解得:P=1681.
b.
最佳策略当然是重新借钱啊,因为利息低了,不用还那么多利息了.
c.
4年后即48个月后,我们要计算现在还有多少钱要还.
此时我们还的48个月的钱,每月还P,在48个月后的价值为:
P(1+9.5%/12)^47+P(1+9.5%/12)^46+...+P(1+9.5%/12)^1+P=97695
而此时原贷款200000的价值为200000*(1+9.5%/12)^48=292019
此时还要还货款的值为292019-97695=194324.
设新利息下每月还钱为Q,则按类似的方式得:
新货款30年(360个月)后的总价值为:
Q(1+6.75%/12)^359+Q(1+6.75%/12)^358+...+Q(1+6.75%/12)^1+Q
而新借的钱194324在360个月后,价值为194324*(1+6.75%/12)^360.
以上两者应相等:
Q(1+6.75%/12)^359+Q(1+6.75%/12)^358+...+Q(1+6.75%/12)^1+Q
=194324*(1+6.75%/12)^360.
解得 Q=1260.
d.
原来应交的钱为:P*360=605160
新方案应交的钱为:P*48+Q*360=534288
所以少交了很多钱-_- 605160-534288=70872
你明白了吗?.
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