To calculate the accumulated value of Sam's retirement investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated value
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, Sam's principal amount (P) is $150,000, the annual interest rate (r) is 5.2% or 0.052 as a decimal, the interest is compounded daily, so the number of times interest is compounded per year (n) is 365, and the investment period (t) is 20 years.
Plugging these values into the formula, we get:
A = 150000(1 + 0.052/365)^(365*20)
Calculating this, the accumulated value (A) for Sam's retirement investment is approximately $423,599.
Rounding to the nearest dollar, the accumulated value for Sam's retirement would be $423,599.