Question

Brandon invested $1,100 in an account paying an interest rate of 7(3)/(4)% compounded continuously. Julian invested $1,100 in an account paying an interest rate of 8(1)/(4)% compounded monthly. After a certain period of time, whose investment will have a higher value? 1) Brandon 2) Julian 3) Both will have the same value 4) Cannot be determined

Answer 1

To determine whose investment will have a higher value, we need to calculate the future value of each investment using the compound interest formula.

Step-by-step explanation:

To determine whose investment will have a higher value, we need to calculate the future value of each investment using the compound interest formula.

For Brandon's investment:

Future Value = $1100 * e^(0.0775 * t) (continuous compounding)

For Julian's investment:

Future Value = $1100 * (1 + 0.0825/12)^(12t) (monthly compounding)

By comparing the calculated future values for different time periods, we can determine whose investment will have a higher value.

Answer 2

To compare the investments of Brandon and Julian, you can calculate the future value of each investment using the formulas for compound interest. Brandon invested $1,100 at an interest rate of 7(3)/(4)% compounded continuously, while Julian invested $1,100 at an interest rate of 8(1)/(4)% compounded monthly. By comparing the future values, you can determine whose investment will have a higher value.

Step-by-step explanation:

To compare the investments of Brandon and Julian, we need to calculate the future value of each investment. Brandon invested $1,100 at an interest rate of 7(3)/(4)% compounded continuously. This can be calculated using the formula for continuous compound interest:

FV = P * e^(rt)

Where FV is the future value, P is the principal amount, e is the base of the natural logarithm, r is the interest rate, and t is the time in years.

For Julian, the interest rate is 8(1)/(4)% compounded monthly, so we can use the formula for compound interest:

FV = P * (1 + r/n)^(nt)

Where FV is the future value, P is the principal amount, r is the interest rate per period, n is the number of compounding periods per year, and t is the time in years.

By calculating the future value of each investment at the same time period, we can determine whose investment will have a higher value.

Here are the calculations:

Brandon's investment: FV = 1100 * e^((7(3)/(4))/100 * t)

Julian's investment: FV = 1100 * (1 + (8(1)/(4))/100/12)^(12 * t)

By comparing the future values of each investment, we can determine which investment will have a higher value.