How long will it take to earn $7000 on a $3500 investment at a rate of 7.8% compounding continuously?

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Answer 1 · 2016-06-12T12:56:24

$n = 9.229$ $n = 9.229$ years

As it does not state what the period of compounding refers to, I will assume it is per year.

For Compound Interest"
$A m o u n t = P {(1 + r)}^{n}$ $Amount = P(1 + r)^n$ , where $n$ $n$ is the time in years.

$7000 = 3500 {(1 + 0.078)}^{n}$ $7000 = 3500(1 + 0.078)^n$

$2 = {(1.078)}^{n} divide by 3500$ $2 = (1.078)^n " divide by 3500"$

Because $n$ $n$ is an exponent, we need to use logs.

$log 2 = n log 1.078 power law as well$ $log2 = n log1.078" power law as well"$

$\frac{log 2}{log 1.078}$ $log2/log1.078$ = $n$ $n$

$n = 9.229 y e a r s calculator$ $n = 9.229 years " calculator"$