Step-by-step explanation:
To calculate the value of the investment after 8 years with daily compounding interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
Given:
P = $4140
r = 7% = 0.07
n = 365 (daily compounding)
t = 8 years
Plugging in the values into the formula, we have:
A = 4140(1 + 0.07/365)^(365*8)
Calculating this expression will give us the value after 8 years:
A ≈ 4140(1.000191)^2920 ≈ 4140(1.676793216) ≈ $6944.45
Therefore, the value of the investment after 8 years, rounded to the nearest penny, is approximately $6944.45.
