Question

For the following amount at the given interest rate compounded continuously, find (a) the future value after 5 years, (b) the interest earned, and (c) the time to reach $17,000. $5300 at 3.6% a. The future value after 5 years is approximately $. (Do not round until the final answer. Then round to the nearest cent as needed.) b. The interest earned is. (Do not round until the final answer. Then round to the nearest cent as needed.) c. The time to reach $17,000 from $5300 at 3.6% is years. (Do not round until the final answer. Then round to three decimal places as needed.)

Answer 1

a). FV = PV * e^{(r * t)}

= $5,300 * e^{(0.036 * 5)}

= $5,300 * e^0.18 = $5,300 * 1.1972 = $6,345.25

b). Interest Earned = Future Value - Present Value = $6,345.25 - $5,300 = $1,045.25

c). n = [log(FV/PV)] / [log(1 + r)]

= [log($17,000/$5,300)] / [log(1 + 0.036)]

= [log(3.2075)] / [log(1.036)]

= 1.1655 / 0.03537 = 32.954 years