Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 5
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Answer:
Her new monthly payment is now $1,378.91¢
Step-by-step explanation:
For us to calculate the new monthly mortgage payment that Anna will start paying from now on, we need to input the formula for calculating monthly mortgage payments.
The formula is:-
Where M is the monthly mortgage payment.
P is the principal
r is the monthly interest rate calculated by dividing your annual interest rate by 12
n is the number of payments(the number of months you will be paying the loan).
In this case, the new principal that Anna must pay back is $231,905.47¢. The annual interest rate has been reduced to 5.17% from 5.75% so the new monthly interest rate will be obtained by dividing the new annual interest rate by 12
= 5.17%/2
= 0.431%
This is the new monthly interest rate.
Since she has been paying her mortgage loan diligently for 5 complete years. It means she now has just 25 years to complete the payment. If 12 months make up one year, then there are - 12 × 25 = 300 more months to go.
300 is therefore "n" that is required for the calculation.
All the terms needed for the calculation of her new monthly mortgage is now complete.
P = $231,905.47¢
r = 0.431%
n = 300
= 231,905.47 × 0.005946
M = $1,378.91¢
Therefore her new monthly mortgage payment will become $1,378.91¢
To be clear, the given relation between
time and female population is an integral:<span>
</span><span>
</span>
</span>
</span>= <span><span>
In order to evaluate this integral, we need to write this rational function in a simpler way:
</span>
</span>where we need to evaluate A and B. In order to do so, let's calculate the LCD:<span>
</span>
</span>the denominators cancel out and we get:<span>
</span>P + 400 = 0.2AP - 400A + BP<span>
</span> = P(0.2A + B) - 400A<span>
</span>The two sides must be equal to each other, bringing the system:<span>
</span>
</span>Which can be easily solved:<span>
</span>
</span>Therefore, our integral can be written as:<span>
</span>
</span>=
</span>=
</span>= - ln |P| + 6 ln |0.2P - 400| + C<span>
</span>Now, let’s evaluate C by considering that at t = 0 P = 10000:<span>
</span>0 = - ln |10000| + 6 ln |0.2(10000) - <span>400| + C
C = ln |10000</span>| - 6 ln |1600|<span>
</span>C = ln (10⁴) - 6 ln (2⁶·5²)<span>
</span>C = 4 ln (10) - 36 ln (2) - 12 ln (5) <span><span>
</span></span><span><span> </span>Therefore, the equation relating female population with time requested is:<span>
</span><span>t = - ln |P| + 6 ln |0.2P - 400| + 4 ln (10) - 36 ln </span>(2) - 12 ln (5)</span></span>