Financial Problem - Compound Interest

[Guest]

Mortgage Loan Amount - $150,000
Number of Years - 15
Interest rate per year - 2.25%

This comes to $982.63 mortgage per month
Total Interest that will be paid to bank over 15 years - $26,872.79

Now lets assume that apart from \$982.63 every month, I have \$600 more which I either want to pay towards mortgage or invest in mutual funds

Should I pay $600 toward mortgage or invest it in mutual fund which gives 8% annual

Which one makes more financial sense. Please show calculation.

Thank you

[Baltuilhe]

Good afternoon!!

I've verified, $982.63 is the correct value.

So, you have $600 more... and a investiment which pays 8% annually?
Against 2.25%? No doubts!

Calculating:
PMT = $ 600,00
n = 180 months (15 years)
i = 8% a.a.

[tex]FV=PMT\cdot\left[\dfrac{\left(1+i\right)^{n}-1}{i}\right]\\
FV=600\cdot\left[\dfrac{\left(1+\dfrac{8\%}{12}\right)^{180}-1}{\dfrac{8\%}{12}}\right]\\
FV\approx 600\cdot\left(\dfrac{1,006667^{180}-1}{0,006667}\right)\\
FV\approx 207\,622,93[/tex]

If you use the $ 600 to 'mortgage', you will pay 982.63 + 600 = 1582.63, right?
[tex]PV=PMT\cdot\left[1-\dfrac{\left(1+i\right)^{-n}}{i}\right]\\
150\,000=1\,582.63\cdot\left[\dfrac{1-\left(1+\dfrac{2.25\%}{12}\right)^{-n}}{\dfrac{2.25\%}{12}}\right]\\
150\,000=1\,582.63\cdot\left(\dfrac{1-1,001875^{-n}}{0,001875}\right)\\
\dfrac{150\,000}{1\,582.63}\cdot 0,001875=1-1,001875^{-n}\\
1,001875^{-n}=1-\dfrac{150\,000\cdot 0,001875}{1\,582.63}\\
n=-\dfrac{\log\left(1-\dfrac{150\,000\cdot 0,001875}{1\,582.63}\right)}{\log\left(1,001875\right)}\\
n\approx 105[/tex]

Now, let's investigate how much money can you earn in 105 months.
[tex]FV=PMT\cdot\left[\dfrac{\left(1+i\right)^{n}-1}{i}\right]\\
FV=600\cdot\left[\dfrac{\left(1+\dfrac{8\%}{12}\right)^{105}-1}{\dfrac{8\%}{12}}\right]\\
FV\approx 600\cdot\left(\dfrac{1,006667^{105}-1}{0,006667}\right)\\
FV\approx 90\,817,21[/tex]

The 'balloon', paying just 982.63:
[tex]PV=PMT\cdot\left[1-\dfrac{\left(1+i\right)^{-n}}{i}\right]\\
PV=982.63\cdot\left[\dfrac{1-\left(1+\dfrac{2.25\%}{12}\right)^{-(180-105)}}{\dfrac{2.25\%}{12}}\right]\\
PV=982.63\cdot\left(\dfrac{1-1,001875^{-75}}{0,001875}\right)\\
PV\approx 68\,690,05[/tex]

Hope to Have Helped!