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.