Recently, a certain bank offered a 5-year CD that earns 3.26% compounded continuously. Use the given information to answer the questions. (a) If $30,000 is invested in this CD, how much will it be worth in 5 years?(Round to the nearest cent.)
(b) How long will it take for the account to be worth $45,000?(Round to two decimal places as needed)

a. The CD will worth $35,311 in five years.

b. It will take 12.44 years for the account to be worth $45,000.

Explanation:

a) If $30,000 is invested in this CD, how much will it be worth in 5 years?(Round to the nearest cent.)

This can be determined using the formula for calculating the future value (FV) compounding formula as follows:

FV = PV * e^(rn) (1)

FV = Future value in five years = ?

PV = Present value of amount invested = $30,000

e = Mathematical constant approximated as 2.7183

r = Interest rate = 3.26%, or 0.0326

n = number of years = 5

Substituting the values into equation (1), we have:

FV = $30,000 * 2.7183^(0.0326 * 5)

FV= $35,311

Therefore, the CD will worth $35,311 in five years.

(b) How long will it take for the account to be worth $45,000?(Round to two decimal places as needed)

Also, using equation (1) part a, we have:

FV = Future value in n years = $45,000

PV = Present value of amount invested = $30,000

e = Mathematical constant approximated as 2.7183

r = Interest rate = 3.26%, or 0.0326

n = number of years it will take to have $45,000 = ?

Substituting the values into equation (1), we have:

$45,000 = $30,000 * 2.7183^(0.0326 * n)

$45,000 / $30,000 = 2.7183^(0.0326 * n)

1.50 = 2.7183^(0.0326 * n)

Loglinearise both sides and solve for n, we have:

Log(1.50) = (0.0326 * n)Log(2.7183)

0.176091259055681 = 0.0326 * n * 0.434297385124509

0.176091259055681 = n * 0.014158094755059

n = 0.176091259055681 / 0.014158094755059

n = 12.44 years

Therefore, it will take 12.44 years for the account to be worth $45,000.

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