QuestionPoints: 4 of 8
Giost
Someone invests in an account at interest compounded annually. Let be the value (in dollars) of the account at t years after she has invested the spo90.
What does it mean in this situation?
A. The account balance increases by .
B. The account balance decreases by per year.
C. The account balance does not change.
D. The account balance increases by per year.
c. What is the initial amount?
3090
What does it mean in this situation?
A. The initial amount in the account was .
B. The final amount in the account after years was .
C. The account balance increases by per year.
D. The account balance decreases by per year.
d. What will be the account's value in 14 years?
\611^{1} 7.99^{*}$ (Type an integer or decimal rounded to the nearest cent as needed.)
You answered:
Studdy Solution
STEP 1
1. The initial investment is \$3090.
2. The interest rate is 5% compounded annually.
3. We need to determine the meaning of the interest rate and calculate the account's value after 14 years.
STEP 2
1. Interpret the meaning of the interest rate in the context of the problem.
2. Identify the initial amount.
3. Calculate the future value of the investment after 14 years.
STEP 3
The interest rate of 5% compounded annually means that each year, the account balance increases by 5% of the current balance.
STEP 4
The initial amount in the account is \$3090. This is the starting balance before any interest is applied.
STEP 5
To calculate the future value of the investment after 14 years, use the compound interest formula: \[ y = P(1 + r)^t $ where \( P = 3090 \), \( r = 0.05 \), and \( t = 14 \).
STEP 6
Substitute the values into the formula:
\[
y = 3090(1 + 0.05)^{14} $
Calculate the expression:
\[
y = 3090(1.05)^{14} $
STEP 7
Compute .
Multiply by the initial amount:
\[
y \approx 3090 \times 1.979 \approx 6117.99 $
The account's value in 14 years is approximately:
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