Question 184696
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Part A.


Actually, you aren't even close.  Just do a quick mental sanity check.  10% of 760000 is 76000, so 5% is half of that or 38000.  If you only got 5% on your original principal and didn't compound you would get 5 times 38000 in 5 years -- nearly $200K.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  FV = P(1 + r)^n]


Where <i>FV</i> is Future Value, <i>P</i> is Principal, <i>r</i> is the interest rate per compounding period, and <i>n</i> is the number of periods. 


For your situation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  FV = 760000(1 + .05)^5 \approx 969973.99]


(Said his calculator, confidently)


If the Future Value is $969,973.99 on an investment of $760,000.00, then the interest earned is the difference between the two or $209,973.99.


Part B.


Continuous compounding requires a different formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  FV = Pe^{rt}]


Where <i>FV</i> is Future Value, <i>P</i> is Principal, <i>e</i> is the base of the natural logarithms (approx. 2.718), <i>r</i> is the interest rate per time period, and <i>t</i> is the number of time periods. 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  FV = 760000\cdot e^{0.05\cdot5} \approx 975859.32]


Again, subtracting the principal, the interest earned is: $215,859.32


So continuous compounding gets you an extra $100 per month over the 5 year period.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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