The nearest ten dollars, you would need to invest approximately $132,140.
Let’s find the amount you need to invest in an account paying an interest rate of 6.2% compounded continuously for the value of the account to reach $182,000 in 10 years.
We can use the formula for continuous compound interest:
A = P * e^(rt)
where:
A is the final amount
P is the initial principal
r is the annual interest rate
t is the time in years
In this case, we have:
A = $182,000
r = 6.2% = 0.062
t = 10 years
Let's solve for P:
P = A / e^(rt)
P = $182,000 / e^(0.062 * 10)
P ≈ $132,136.46
Rounding to the nearest ten dollars, you would need to invest approximately $132,140.