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Compound interest is the addition of interest on the interest of the principal amount.
<h3>What is compound interest?</h3>Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,
As it is given that the principal amount is $15,000; while the rate of interest is 2.8%, and the amount is invested for a period of 5 years.
A.) When the interest is charged weekly,
As we know that there are 52 weeks in a year, therefore, n = 52, substitute the values,
B.) When the interest is charged daily,
As we know that there are 365 days in a year, therefore, n = 365, substitute the values,
C.) When the interest is charged Continuously,
As we know that the formula for continuous compounding is given as,
Substitute the values, we will get,
D.) When the interest is charged Monthly,
As we know that there are 12 months in a year, therefore, n = 12, substitute the values,
E.) When the interest is charged Semi-annually,
As we know that the interest is charged Semi-annually, therefore, n = 2, substitute the values,
F.) When the interest is charged Quarterly,
As we know that the interest is charged Quarterly, therefore, n = 4, substitute the values,
Learn more about Compound Interest:
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Answer:
63.7% or 33.35 miles
Step-by-step explanation:
The hint suggests that we find the points where the drive begins and ends picking up the transmitter. We suspect both of those points will have irrational coordinates, so finding the distance between them will involve dealing with squares and roots of irrational numbers. We want to see if there's an easier way.
The distance from the transmitter to the path being driven can be found using the "distance to a line" formula. First, we need the equation of the line in general form. In intercept form, it is ...
y/38 +x/36 = 1
19x +18y -684 = 0 . . . . . . multiply by LCM(36, 38) and subtract that amount
Then the distance from the origin to the line is ...
d = |19·0 +18·0 -684|/√(19² +18²) = 685/√685 ≈ 26.1243
The distance (x) along the line from the point where the transmitter is first picked up until the point of closest approach can be found from the Pythagorean theorem:
x² + (26.1243)² = 31²
x² = 31² -(684/√685)² = 190429/685
x ≈ 16.6733
The driving distance for which the transmitter is picked up is twice this, so is ...
2x = 2(16.6733) ≈ 33.3466 . . . miles
The total drive length is also given by the Pythagorean theorem:
drive length = √(36² +38²) = √2740 ≈ 52.3450 . . . miles
Then the fraction of the drive during which the signal is picked up is ...
fraction = (33.3466 mi)/(52.3450 mi) ≈ 0.6371 ≈ 63.7%
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The signal is picked up for 33.35 miles, about 63.7% of the drive.
______
The intercept-form equation for a line is ...
x/(x-intercept) +y/(y-intercept) = 1
The distance from (x, y) to line ax+by+c=0 is given by ...
d = |ax+by+c|/√(a²+b²)
The Pythagorean theorem relates legs a, b and hypotenuse c of a right triangle this way:
c² = a² +b²
