Final answer:
The current value of a $200,000 loan after 8 years with a 5% annual compound interest rate is calculated using the formula A = P(1 + r/n)^(nt), which takes into account the principal amount, interest rate, compounding frequency, and time.
Step-by-step explanation:
To calculate the current value of a loan with compound interest, you can use the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for, in years.
In this case, the principal amount P is $200,000, the annual interest rate r is 5% or 0.05, n is 1 (since the interest is compounded annually), and the time t is 8 years.
The formula becomes: A = $200,000(1 + 0.05/1)^(1*8) = $200,000(1 + 0.05)^8
Calculating this will give you the current value of the loan after 8 years with a 5% compounded annual interest rate.