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How long will it take a $138,450 investment to grow to $148.540 if money earns 3.98% compounded quarterly? Use I/Y=3.98,P/Y=4, PMT =0.

User Jennice
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1 Answer

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It will take approximately 5 years for the $138,450 investment to grow to $148,540 with a 3.98% annual interest rate compounded quarterly. To calculate the time it will take for an investment to grow to a specific amount, we can use the formula for compound interest: A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment
P = the initial investment amount
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years

In this case, the initial investment (P) is $138,450 and the future value (A) is $148,540. The interest rate (r) is 3.98% or 0.0398, and interest is compounded quarterly, so n = 4.

Now, let's solve for t, the number of years:


148,540 = 138,450(1 + 0.0398/4)^(4t)


To simplify the equation, let's divide both sides by 138,450:

148,540/138,450 = (1 + 0.0398/4)^(4t)

1.071937 = (1 + 0.00995)^(4t)

Now, let's take the natural logarithm (ln) of both sides to isolate t:

ln(1.071937) = ln((1 + 0.00995)^(4t))

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

ln(1.071937) = 4t * ln(1 + 0.00995)

Now, divide both sides by 4 * ln(1 + 0.00995):

t = ln(1.071937) / (4 * ln(1 + 0.00995))

Using a calculator, we find that t ≈ 5.00002 years.

So the time it will take is 5 years.

User Nuibb
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