Question

Part A

Which account will have a greater value after 10 years?

Account information for two accounts. Account A has principal 16 thousand dollars, annual interest 3 percent, compounded quarterly for number of years equals 10. Account B has principal 16 thousand dollars, annual interest 3 percent, compounded monthly for number of years equals 10.
A. Account A
B. Account B
What will the value of that account be after 10 years?

$

Part B

What type of growth do both accounts model?
A. linear
B. exponential
C. neither

Answer 1

Account B, which compounds monthly, will have a greater value after 10 years compared to Account A, which compounds quarterly, due to the effects of more frequent compounding. The value of both accounts grows exponentially over time.

Step-by-step explanation:

When comparing two interest-bearing accounts with the same principal, rate of interest, and time period, the account with more frequent compounding will ultimately have a greater value. For Account A, which compounds quarterly, the formula to calculate the future value is P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Applying the values for Account A, we have 16000(1 + 0.03/4)^(4*10).

For Account B, which compounds monthly, the same formula is used but n changes to 12. So, we calculate 16000(1 + 0.03/12)^(12*10). Compounding more frequently results in a higher future value, thus Account B, which compounds monthly, will have a greater value after 10 years.

The growth of both accounts is exponential because the amount of money grows at a rate proportional to its current value, where the compounding effect increases the total amount exponentially over time.

After calculating using the formula, Account B's value after 10 years would exceed that of Account A.

Answer 2

Both models are exponential

A: $21,573.58

B: $21,589.58

Step-by-step explanation:

A

f(x) = 16,000
`(1 + .03/4)^(4(10))`

f(x) = (16000)
`1.0075^(40)`

f(x) = $21,573.58 Rounded to the nearest cent.

B

f(x) = 16000
`(1+ .03/12)^(12(10))`

f(x) = (16000)
`1.0025^(120)`

f(x) = $21,589.66 Rounded to the nearest cent