Question

**a.** What is the future value in six years of
$1,400 invested in an account with an annual percentage rate of 9
percent, compounded annually? **(Do not round intermediate
calculations and round your answer to 2 decimal places, e.g.,
32.16.)**

Future value $

**b.** What is the future value in six years of $1,400
invested in an account with an annual percentage rate of 9 percent,
compounded semiannually? **(Do not round intermediate
calculations and round your answer to 2 decimal places, e.g.,
32.16.)**

Future value $

**c.** What is the future value in six years of $1,400
invested in an account with an annual percentage rate of 9 percent,
compounded monthly? **(Do not round intermediate calculations
and round your answer to 2 decimal places, e.g.,
32.16.)**

Future value $

**d.** What is the future value in six years of $1,400
invested in an account with an annual percentage rate of 9 percent,
compounded continuously? **(Do not round intermediate
calculations and round your answer to 2 decimal places, e.g.,
32.16.)**

Future value $

Answer #1

**Solution a:**

Principal amount = $1,400

rate of interest = 9% compounded annually

Period = 6 years

Future value = P (1+r)^t = $1,400 (1+0.09)^6 = $1,400 * 1.6771 = $2,347.94

**Solution b:**

Principal amount = $1,400

rate of interest = 9% compounded semi annually, semi annual rate of interest = 9*6/12 = 4.5%

Time = 6 years, semiannual period = 6*2 =12

Future value = P (1+r)^t = $1,400 (1+0.045)^12 = $1,400 * 1.6959 = $2,374.23

**Solution c:**

Principal amount = $1,400

rate of interest = 9% compounded monthly, monthly rate of interest = 9/12 = 0.75%

Time = 6 years, monthly period = 6*12 =72

Future value = P (1+r)^t = $1,400 (1+0.0075)^72 = $1,400 * 1.7125 = $2,397.50

**Solution d:**

Principal amount = $1,400

Rate of interest = 9% compounded continuously

Period = 6 years

Future value = P * e^rt = $1,400 (2.71828)^(0.09*6) = $1,400 * 1.7160 = $2,402.40

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Future value $ Not attempted
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