Question

You want to invest $ 14450 in an account and plan to leave it there for 7 years. there are three options for investing your money.

a) pays 6.5% interest per year, compounded semiannually ( 2 times per year).
b) pays 6.5% interest per year, compounded monthly ( 12 times per year).
c) pays 6.5% interest per year, compounded four times per day ( 1460 times per year).

Answer 1

This question relates to the calculation of the future value of an investment using the compound interest formula for different compounding intervals. By applying the compound interest formula with various compounding frequencies , students can determine the future value of a seven-year investment at 6.5% annual interest.

Step-by-step explanation:

The question involves the calculation of future value of an investment with compound interest. To find out how much money one would have after investing $14,450 for 7 years at 6.5% interest, compounded at different intervals, we would use the compound interest 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 (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

In this case, for option (a), which is compounded semiannually, n would be 2; for option (b), which is compounded monthly, n would be 12; and for option (c), which is compounded four times per day, n would be 1460. These calculations would provide answers for each compounding interval, demonstrating the effects of different compounding frequencies on the future value of the investment.