QuestionJuly 27, 2025

Over 2 years, how much more does 2000 in a savings account with an APR of 5.2% compounded quarterly earn in interest than the same amount in a savings account with an APR of 4.8% compounded monthly? A. 8.31 B. 4.15 C. 33.22 D. 16.61

Over 2 years, how much more does 2000 in a savings account with an APR of 5.2% compounded quarterly earn in interest than the same amount in a savings account with an APR of 4.8% compounded monthly? A. 8.31 B. 4.15 C. 33.22 D. 16.61
Over 2 years, how much more does 2000 in a savings account with an APR of 5.2% compounded quarterly earn in interest than the same amount in a savings account with an APR of 4.8% compounded monthly? A. 8.31 B. 4.15 C. 33.22 D. 16.61

Solution
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Answer

\ 19.31 Explanation 1. Calculate interest for 5.2% APR compounded quarterly Use the formula for compound interest: **A = P \left(1 + \frac{r}{n}\right)^{nt}**. Here, P = 2000, r = 0.052, n = 4, t = 2. Calculate A and subtract P to find interest. A = 2000 \left(1 + \frac{0.052}{4}\right)^{4 \times 2} = 2000 \left(1 + 0.013\right)^8 = 2000 \times 1.1094 = 2218.80 Interest = 2218.80 - 2000 = 218.80 2. Calculate interest for 4.8% APR compounded monthly Use the same formula with r = 0.048, n = 12. Calculate A and subtract P to find interest. A = 2000 \left(1 + \frac{0.048}{12}\right)^{12 \times 2} = 2000 \left(1 + 0.004\right)^{24} = 2000 \times 1.0996 = 2199.49 Interest = 2199.49 - 2000 = 199.49 3. Calculate the difference in interest Subtract the interest from the second account from the first. Difference = 218.80 - 199.49 = 19.31

Explanation

1. Calculate interest for 5.2% APR compounded quarterly<br /> Use the formula for compound interest: **$A = P \left(1 + \frac{r}{n}\right)^{nt}$**. Here, $P = 2000$, $r = 0.052$, $n = 4$, $t = 2$. Calculate $A$ and subtract $P$ to find interest.<br /> $A = 2000 \left(1 + \frac{0.052}{4}\right)^{4 \times 2} = 2000 \left(1 + 0.013\right)^8 = 2000 \times 1.1094 = 2218.80$<br /> Interest = $2218.80 - 2000 = 218.80$<br /><br />2. Calculate interest for 4.8% APR compounded monthly<br /> Use the same formula with $r = 0.048$, $n = 12$. Calculate $A$ and subtract $P$ to find interest.<br /> $A = 2000 \left(1 + \frac{0.048}{12}\right)^{12 \times 2} = 2000 \left(1 + 0.004\right)^{24} = 2000 \times 1.0996 = 2199.49$<br /> Interest = $2199.49 - 2000 = 199.49$<br /><br />3. Calculate the difference in interest<br /> Subtract the interest from the second account from the first.<br /> Difference = $218.80 - 199.49 = 19.31$
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