To calculate the value of the investment in the year 2012, we need to know how many years the money was invested. Assuming the investment was made in 1852 and the year 2012, the number of years is 2012 - 1852 = 160.
Compounded annually:
The formula for calculating the future value of an investment with annual compounding is FV = PV x (1 + r)^n, where FV is the future value, PV is the present value, r is the annual interest rate as a decimal, and n is the number of years. Plugging in the values, we get FV = 30 x (1 + 0.06)^160 = $1,342,669.42.
Compounded monthly:
The formula for calculating the future value of an investment with monthly compounding is FV = PV x (1 + r/12)^(n x 12), where FV is the future value, PV is the present value, r is the annual interest rate as a decimal, and n is the number of years. Plugging in the values, we get FV = 30 x (1 + 0.06/12)^(160 x 12) = $1,380,935.15.
Compounded daily:
The formula for calculating the future value of an investment with daily compounding is FV = PV x (1 + r/365)^(n x 365), where FV is the future value, PV is the present value, r is the annual interest rate as a decimal, and n is the number of years. Plugging in the values, we get FV = 30 x (1 + 0.06/365)^(160 x 365) = $1,388,628.12.