Financial Maths Question (1 Viewer)

Shuuya · Apr 25, 2016

Question:

A person borrows $200,000 from the bank to put down the deposit for a new house at a rate of 9% per annum, compounded monthly. At the end of the month, she pays back $5000. Find how long it takes to repay the loan, correct to the nearest month.

Thanks!

leehuan · Apr 25, 2016

${ A }_{ 1 }=200000\left( 1.0075 \right) -5000\\ \vdots \\ { A }_{ n }=200000{ \left( 1.0075 \right) }^{ n }-5000\left( 1+1.0075+{ 1.0075 }^{ 2 }+\dots +{ 1.0075 }^{ n-1 } \right)$

Please make sure in the exam you write up to A₃ as well

$We request that {A}_{n}=0$

$\begin{align*} \therefore 0&=200000{ \left( 1.0075 \right) }^{ n }-5000\left( \frac { { 1.0075 }^{ n }-1 }{ 1.0075-1 } \right) \\ \Leftrightarrow 0&=200{ \left( 1.0075 \right) }^{ n }-5\left( \frac { { 1.0075 }^{ n }-1 }{ 1.0075-1 } \right) \\ \Leftrightarrow \frac { 2000 }{ 3 } \left( { 1.0075 }^{ n }-1 \right) &=200{ \left( 1.0075 \right) }^{ n }\\ \Leftrightarrow -\frac { 2000 }{ 3 } &=-\frac { 1400 }{ 3 } { \left( 1.0075 \right) }^{ n }\\ \Leftrightarrow \frac { 10 }{ 7 } &={ \left( 1.0075 \right) }^{ n }\\ \Leftrightarrow \ln { \frac { 10 }{ 7 } } &=n\ln { 1.0075 } \end{align*}$

Subject to inaccuracy

Shuuya · Apr 25, 2016

leehuan said:
${ A }_{ 1 }=200000\left( 1.0075 \right) -5000\\ \vdots \\ { A }_{ n }=200000{ \left( 1.0075 \right) }^{ n }-5000\left( 1+1.0075+{ 1.0075 }^{ 2 }+\dots +{ 1.0075 }^{ n-1 } \right)$

Please make sure in the exam you write up to A₃ as well

$We request that {A}_{n}=0$

$\begin{align*} \therefore 0&=200000{ \left( 1.0075 \right) }^{ n }-5000\left( \frac { { 1.0075 }^{ n }-1 }{ 1.0075-1 } \right) \\ \Leftrightarrow 0&=200{ \left( 1.0075 \right) }^{ n }-5\left( \frac { { 1.0075 }^{ n }-1 }{ 1.0075-1 } \right) \\ \Leftrightarrow \frac { 2000 }{ 3 } \left( { 1.0075 }^{ n }-1 \right) &=200{ \left( 1.0075 \right) }^{ n }\\ \Leftrightarrow -\frac { 2000 }{ 3 } &=-\frac { 1400 }{ 3 } { \left( 1.0075 \right) }^{ n }\\ \Leftrightarrow \frac { 10 }{ 7 } &={ \left( 1.0075 \right) }^{ n }\\ \Leftrightarrow \ln { \frac { 10 }{ 7 } } &=n\ln { 1.0075 } \end{align*}$

Subject to inaccuracy

Thanks! Makes sense now

eyeseeyou · May 13, 2016

Shuuya said:
Question:

A person borrows $200,000 from the bank to put down the deposit for a new house at a rate of 9% per annum, compounded monthly. At the end of the month, she pays back $5000. Find how long it takes to repay the loan, correct to the nearest month.

Thanks!

Is this series and sequences?

Nailgun · May 13, 2016

eyeseeyou said:
Is this series and sequences?

It's rates and finance, which is a related topic but separate

eyeseeyou · May 15, 2016

Nailgun said:
It's rates and finance, which is a related topic but separate

Which textbook is it in?

jathu123 · May 15, 2016

eyeseeyou said:
Which textbook is it in?

idk about other books but I guess it should be in most of them , but in the Cambridge 3u yr 12 book, its the chapter 7. 7A-7D is the application of series and sequences for the finance topic like loan and stuff

Financial Maths Question (1 Viewer)

Shuuya

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leehuan

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Shuuya

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eyeseeyou

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Nailgun

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eyeseeyou

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jathu123

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