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3 years ago

How long will it take for an investment to triple, if interest is compounded continuously at 8%?

Mathematics

1 answer:

maw [93]3 years ago

6 0

Answer:

<em>It will take 14 years before the investment triples</em>

Step-by-step explanation:

<u>Continuous Compounding</u>

Is the mathematical limit that compound interest can reach if it was calculated and reinvested into an account's balance over a theoretically infinite number of periods.

The formula for continuous compounding is derived from the formula for the future value of a compound interest investment:

$FV = PV\cdot e^{i.t}$

Where:

FV = Future value of the investment

PV = Present value of the investment

i = Interest rate

t = Time

It's required to find the time for an investment to triple, that is, FV = 3 PV, knowing the interest rate is i=8%=0.08.

Substituting the known values:

$3PV = PV\cdot e^{i.t}$

Dividing by PV:

$3 = e^{i.t}$

Taking logarithms:

$\ln 3=i.t$

Solving for t:

$\displaystyle t=\frac{\ln 3}{i}$

$\displaystyle t=\frac{\ln 3}{0.08}$

t = 13.7 years

Rounding up:

It will take 14 years before the investment triples

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vredina [299]

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3 years ago

the ratio of the areas of two similar polygons is 81:64. If the perimeter of the first polygon is 32 cm, what is the perimeter o

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In two similar polygons, the ratio of their areas is the square of the ratio of their sides. If the sides of any polygon are a and b then :

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Given ratio of area =81:64

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Cross multiplying

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