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You have $50,000 in savings for retirement in an investment earning 2% annually. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal?

Please round your answer to the nearest hundredth.

User Fatihk
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Answer: To determine how many years it will take to reach your retirement goal of $1,000,000 with an initial investment of $50,000 and an annual interest rate of 2%, we can use the compound interest formula:

Future Value = Present Value × (1 + r)^n

where:

Future Value = $1,000,000 (your retirement goal)

Present Value = $50,000 (your initial investment)

r = annual interest rate (in decimal form, 2% = 0.02)

n = number of years (unknown, what we want to find)

Now, plug in the values:

$1,000,000 = $50,000 × (1 + 0.02)^n

To find the value of "n," we need to isolate it on one side of the equation. Divide both sides by $50,000:

20 = (1.02)^n

Now, take the logarithm of both sides to solve for "n":

log(20) = log((1.02)^n)

Using the logarithm properties, we can bring the exponent "n" down:

log(20) = n * log(1.02)

Now, solve for "n":

n = log(20) / log(1.02)

Using a calculator, calculate the value of "n":

n ≈ 35.006

So, it will take approximately 35.01 years (rounded to the nearest hundredth) to reach your retirement goal of $1,000,000 with an initial investment of $50,000 and an annual interest rate of 2%, assuming you add no more to your savings.

User Paulo Soares
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