QuestionJune 13, 2025

If 5000 is borrowed at a rate of 6.75% interest per year, compounded quarterly, find the amount due at the end of the given number of years. (Round your answers to the nearest cent.) (a) 3 years square (b) 5 years square (c) 7 years square

If 5000 is borrowed at a rate of 6.75% interest per year, compounded quarterly, find the amount due at the end of the given number of years. (Round your answers to the nearest cent.) (a) 3 years square (b) 5 years square (c) 7 years square
If 5000 is borrowed at a rate of 6.75%  interest per year, compounded quarterly, find the amount due at the end of the given number of years. (Round
your answers to the nearest cent.)
(a) 3 years
 square 
(b) 5 years
 square 
(c) 7 years
 square

Solution
3.9(222 votes)

Answer

(a) \6098.97 ### (b) \7049.00 ### (c) \8146.71 Explanation 1. Identify the formula for compound interest Use the formula for compound interest: **A = P \left(1 + \frac{r}{n}\right)^{nt}**, where A is the amount, 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 time in years. 2. Calculate for 3 years Given P = 5000, r = 0.0675, n = 4, t = 3. Substitute into the formula: A = 5000 \left(1 + \frac{0.0675}{4}\right)^{4 \times 3}. 3. Calculate for 5 years Given t = 5. Substitute into the formula: A = 5000 \left(1 + \frac{0.0675}{4}\right)^{4 \times 5}. 4. Calculate for 7 years Given t = 7. Substitute into the formula: A = 5000 \left(1 + \frac{0.0675}{4}\right)^{4 \times 7}.

Explanation

1. Identify the formula for compound interest<br /> Use the formula for compound interest: **$A = P \left(1 + \frac{r}{n}\right)^{nt}$**, where $A$ is the amount, $P$ is the principal, $r$ is the annual interest rate, $n$ is the number of times interest is compounded per year, and $t$ is the time in years.<br /><br />2. Calculate for 3 years<br /> Given $P = 5000$, $r = 0.0675$, $n = 4$, $t = 3$. Substitute into the formula: <br />$A = 5000 \left(1 + \frac{0.0675}{4}\right)^{4 \times 3}$.<br /><br />3. Calculate for 5 years<br /> Given $t = 5$. Substitute into the formula: <br />$A = 5000 \left(1 + \frac{0.0675}{4}\right)^{4 \times 5}$.<br /><br />4. Calculate for 7 years<br /> Given $t = 7$. Substitute into the formula: <br />$A = 5000 \left(1 + \frac{0.0675}{4}\right)^{4 \times 7}$.
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