Mathematics, 14.09.2021 19:00 iuthvK5866

A bank offers an account with a 5% annual interest rate, compounded continuously. Approximately how long would it take for a $5,000 investment to double?

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Answer from: xojade

9514 1404 393

13.9 years

Step-by-step explanation:

The doubling time in years for an account earning interest continuously is given exactly by the formula ...

t = 69.31472/r . . . . where r is the annual interest rate in percent

We have r = 5, so the doubling time is ...

t = 69.31472/5 = 13.8629 . . . years

It will take approximately 13.9 years for the investment to double in value.

Additional comment

The account multiplier for continuous interest is ...

e^(rt)

That multiplier is 2 when ...

2 = e^(rt)

ln(2) = rt . . . take the natural log of both sides

t = ln(2)/r = 0.6931472/r

Multiplying by 100 so r is in percent, this is ...

t = 69.31472/r . . . . with r in percent

This compares with the "rule of 72" that is used to estimate doubling time when interest is paid periodically. That rule would tell you doubling time at 5% is approximately 72/5 = 14.4 years. The value "72" actually depends on interest rate and frequency of compounding, so that rule only gives a crude estimate.

Answer from: Quest

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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A bank offers an account with a 5% annual interest rate, compounded continuously. Approximately how...