Question

This Question: 1 pt 3 of 24 (2 complete) Recently, a certain bank offered a 5-year CD that earns 12.15% compounded continuously. Use the given information to answer the questions. (a) If $20,000 is invested in this CD, how much will it be worth in 5 years? approximately $ (Round to the nearest cent.) (b) How long will it take for the account to be worth $50,000? approximately years (Round to two decimal places as needed.)

Answer 1

(a) Here, we will use the following formula of continuous compounding:

FV = PV * e^(i*t)

where, FV is the future value, PV = Present value = $20000, i = rate of interest = 12.15%, t is the time period = 5 and e is the exponential factor whose value is 2.7183

Putting the values in the above formula, we get,

FV = $20000 * (2.7183)^{5 * 12.15%}

FV = $20000 * (2.7183)^0.6075

FV = $20000 * 1.83584352234

FV = $36716.87

So, after 5 years, amount will be $36716.87

(b) Here, we will use the following formula of continuous compounding:

FV = PV * e^(i*t)

where, FV is the future value = $50000, PV = Present value = $20000, i = rate of interest = 12.15%, t is the time period and e is the exponential factor whose value is 2.7183

Putting the values in the above formula, we get,

$50000 = $20000 * (2.7183)^{n * 12.15%}

$50000 / $20000 = (2.7183)^{n * 12.15%}

2.5 = (2.7183)^{n * 12.15%}

(2.7183)^0.917 = (2.7183)^{n * 12.15%}

n * 12.15% = 0.917

n = 0.917 / 12.15%

n = 7.55

So, it will take 7.55 years