Question

If a sum invested gains 10% each year how long will it be before it has doubled its value?

Answer 1

Using an exponential equation, it is found that it will be 7.3 years before the value is doubled.

The equation for an increasing exponential function is given by:

$A(t) = A(0)(1 + r)^t$

In which:

• A(0) is the initial amount.
• r is the growth rate, as a decimal.

In this problem:

• Gains 10% each year, thus $r = 0.1$.

The doubling time is t for which $A(t) = 2A(0)$, then:

$A(t) = A(0)(1.1)^t$

$2A(0) = A(0)(1.1)^t$

$(1.1)^t = 2$

$\log{(1.1)^t} = \log{2}$

$t\log{1.1} = \log{2}$

$t = \frac{\log{2}}{\log{1.1}}$

$t = 7.3$

It will be 7.3 years before the value is doubled.

A similar problem is given at brainly.com/question/23008760