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How long will it take $3100 to grow into $4395.65 if it’s invested at 3.2% compounded annually?

a) 4 years
b) 5 years
c) 6 years
d) 7 years

User Sartori
by
7.9k points

1 Answer

3 votes

Final answer:

It will take approximately 6 years for $3100 to grow into $4395.65 at a 3.2% annual interest rate compounded annually.

Step-by-step explanation:

To find out how long it will take for $3100 to grow into $4395.65 with a 3.2% annual interest rate compounded annually, we can use the formula:

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

Where:

  • A is the final amount ($4395.65)
  • P is the starting principal ($3100)
  • r is the annual interest rate (3.2% as a decimal, or 0.032)
  • n is the number of times interest is compounded per year (in this case, once)
  • t is the number of years

Let's solve for t by rearranging the formula:

$4395.65 = $3100(1 + 0.032/1)^(1*t)

Simplifying:

$4395.65 = $3100(1.032)^t

Dividing both sides by $3100:

(1.4165) = (1.032)^t

Now we need to solve for t. We can use logarithms for this. Taking the logarithm (base 1.032) of both sides:

log(1.4165) / log(1.032) = t

Using a calculator, we find that t ≈ 6.

Therefore, it will take approximately 6 years for $3100 to grow into $4395.65 at a 3.2% annual interest rate compounded annually.

User Pedro Trujillo
by
8.7k points
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