Question
The principal \( P \) is borrowed at simple interest rate \( r \) for a period of time \( t \). Find the loan's future value, \( A \), or the total amount due at time \( t \) \( P=\$ 4000, r=4.5 \%, t=9 \) months The future value is \( \$ \square \). (Simplify your answer. Type an integer or a decimal.)
Ask by Gibson Graham. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The future value is \$4,135.
Solution
To find the future value A using simple interest, we use the formula:
A = P + (P × r × t)
Here,
P = $4000,
r = 4.5% = 0.045 (as a decimal),
t = 9 months = 9/12 = 0.75 years.
Calculate the interest:
Interest = 4000 × 0.045 × 0.75 = 4000 × 0.03375 = 135
Now, the future value is:
A = 4000 + 135 = 4135
The future value is $4135.
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Simplify this solution Beyond the Answer
To find the future value \( A \) using the simple interest formula, we first need to calculate the interest earned over the loan period. The formula for simple interest is: \[ I = P \times r \times t \] Where: - \( P = 4000 \) (the principal) - \( r = 0.045 \) (the annual interest rate expressed as a decimal) - \( t = \frac{9}{12} = 0.75 \) (the loan period in years) Now, let's calculate the interest: \[ I = 4000 \times 0.045 \times 0.75 = 135 \] Next, we find the future value \( A \): \[ A = P + I = 4000 + 135 = 4135 \] So, the future value is \( \$ 4135 \).
