Consider a certificate of deposit that pays 14% (annual percentage rate)on an initial deposit of $3,000.The balance after 14 years is Estimate ,where x is the length of the compounding period (in years).Round your answer to the nearest hundredth.
A) 21,297.98
B) 1,103.64
C) 42,000
D) 3,420
E) 3,000

Question

Consider a certificate of deposit that pays 14% (annual percentage rate)on an initial deposit of $3,000.The balance after 14 years is  Estimate  ,where x is the length of the compounding period (in years).Round your answer to the nearest hundredth. ​​
A) ​21,297.98 
B) ​1,103.64 
C) ​42,000 
D) ​3,420 
E) ​3,000

Quizplus · Accepted Answer

We can use the formula:
A = P(1 + r/n)^(nt)
where A = final balance, P = initial deposit, r = annual percentage rate, n = number of times compounded per year, and t = number of years.
Plugging in the given values, we get:
11,897.70 = 3,000(1 + 0.14/x)^(14x)
Taking the natural logarithm of both sides, we get:
ln(11,897.70/3,000) = 14 ln(1 + 0.14/x)
Dividing both sides by 14, we get:
ln(11,897.70/3,000)/14 = ln(1 + 0.14/x)
Using a calculator, we can solve for x:
x ≈ 0.179
Rounding to two decimal places, we get x ≈ 0.18.
Therefore, the correct answer is A) 21,297.98.

Consider a Certificate of Deposit That Pays 14% (Annual Percentage