Question

Recently, a certain bank offered a 10-year CD that earns 11.86% compounded continuously.

Use the given information to answer the questions.
A. If $10,000 is invested in this CD, how much will it be worth in 10 years? approximately $ (Round to the nearest cent.)
B. How long will it take for the account to be worth $35,000? approximately years? (Round to two decimal places as needed.)

Answer 1

Explanation:

Given the following :

Compounding interest on CD (r) = 11.86%

Period (t) = 10 years

A) If $10,000 is invested in the CD ; worth in 10 years will be ;

A = P(1 + r)^t

Here, P = $10,000

A = final amount or worth

A = 10,000(1 + 0.1186)^10

A = 10,000(1.1186)^10

A = 10,000 × 3.067242759

A = $30672.43

B. How long will it take for the account to be worth $35,000?

A = $35,000 final worth

35000 = 10,000(1 + 0.1186)^t

35000 = 10000(1.1186)^t

Divide both sides by 10000

1.1186^t = 3.5

t = 3.5 / In(1.1186)

t = 3.5 / 0.1120779

t = 31.228

t = 31. 23years