Question

what is the future value in seven years of $1,300 invested in an account with an apr of 8 percent, compounded annually? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. what is the future value in seven years of $1,300 invested in an account with an apr of 8 percent, compounded semiannually? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. what is the future value in seven years of $1,300 invested in an account with an apr of 8 percent, compounded monthly? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) d. what is the future value in seven years of $1,300 invested in an account with an apr of 8 percent, compounded continuously? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The future value of $1,300 invested at an APR of 8% for seven years varies depending on the compounding frequency: annually, it's $2,289.72; semiannually, it's $2,348.89; monthly, it's $2,397.22; and continuously, it's $2,430.77.

Step-by-step explanation:

To calculate the future value of an investment 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, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for.

Future Value with Annual Compounding

For an APR of 8% compounded annually, the formula simplifies to A = $1,300(1 + 0.08/1)^(1*7) = $1,300 * (1.08)^7, which calculates to $2,289.72.

Future Value with Semiannual Compounding

With semiannual compounding, the formula becomes A = $1,300(1 + 0.08/2)^(2*7) = $1,300 * (1.04)^14, resulting in $2,348.89.

Future Value with Monthly Compounding

For monthly compounding, use A = $1,300(1 + 0.08/12)^(12*7) = $1,300 * (1.0066667)^84, and the future value is $2,397.22.

Future Value with Continuous Compounding

To calculate continuous compounding, use the formula A = $1,300e^(0.08*7), where e is the constant approximately equal to 2.71828. This gives a future value of $2,430.77.