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4 votes
You put $500

$
500
in your bank account.
With an interest rate of 5%
5
%
, how long will it take the account to reach $600
$
600
?

1 Answer

4 votes

Answer:

IG: yiimbert

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = final amount ($600)

P = principal amount ($500)

r = annual interest rate (5% or 0.05 as a decimal)

n = number of times interest is compounded per year (we'll assume it's compounded monthly, so n = 12)

t = time in years

Substituting the given values, we get:

$600 = $500(1 + 0.05/12)^(12t)

Dividing both sides by $500, we get:

1.2 = (1 + 0.05/12)^(12t)

Taking the natural logarithm (ln) of both sides, we get:

ln(1.2) = ln[(1 + 0.05/12)^(12t)]

Using the property of logarithms, we can bring the exponent down:

ln(1.2) = (12t) ln(1 + 0.05/12)

Dividing both sides by 12 ln(1 + 0.05/12), we get:

t = ln(1.2) / [12 ln(1 + 0.05/12)]

Using a calculator, we can evaluate this expression and find that:

t ≈ 2.26 years

Therefore, it will take approximately 2.26 years for the account to reach $600 with an interest rate of 5% and monthly compounding.

User Ikumi
by
7.6k points

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