Final answer:
The present value of $5,000 invested for 10 years at a 12% annual interest rate compounded monthly is approximately $1,609.15. The calculation involves the present value formula for compound interest, accounting for the compounding periods and the total investment duration.
Step-by-step explanation:
Calculating the Present Value
To calculate the present value of an investment, we must know the future value, the interest rate, the number of compounding periods, and the total duration of the investment. The question at hand involves finding the present value of $5,000 that is to be received in 10 years with an interest rate of 12% compounded monthly. To solve this, we use the present value formula for compound interest:
PV = FV / (1 + r/n)^(nt)
where:
PV = Present Value
FV = Future Value, which is $5,000 in this case
r = annual interest rate (12% or 0.12)
n = number of times the interest is compounded per year (monthly compounding means n = 12)
t = number of years the money is invested (10 years)
Plugging in the values, we calculate:
PV = $5,000 / (1 + 0.12/12)^(12*10)
PV = $5,000 / (1 + 0.01)^(120)
PV = $5,000 / (1.01)^120
PV ≈ $5,000 / 3.106
PV ≈ $1,609.15
Thus, the present value of $5,000 invested for 10 years at 12% interest compounded monthly is approximately $1,609.15.