2020年6月6日，Elijah在一家银行投资了一笔资金，该银行支付的年单利率为3.5%。他在2023年6月6日共收到了 $680.40 的利息。 求Elijah在银行投资的金额。 答案 $... Freddy在另一家银行投资了 $8000，该银行支付的年复利率为1.75%，按季度复利。 求Freddy在5年末收到的总金额。答案精确到分。 答案 $...

1. Find the time period of the investment in years and write the simple interest relation.

From 6 June 2020 to 6 June 2023, the time is $3$ years.

For simple interest,
$I = Prt$
where $I=680.40$, $r=3.5\%=0.035$, and $t=3$.

2. Rearrange and calculate the principal invested.

$680.40 = P(0.035)(3)$
$680.40 = 0.105P$
$P = \frac{680.40}{0.105}=6480$

1. Find the quarterly interest rate and the total number of compounding periods.

Since the interest is compounded quarterly,

$\text{quarterly rate}=\frac{1.75\%}{4}=0.4375\%$

Over 5 years,

$\text{number of quarters}=5\times 4=20$

2. Apply the compound interest formula and round to the nearest cent.

$A=8000\left(1+\frac{0.4375}{100}\right)^{20}$

$A=8000(1.004375)^{20}$

$A=8729.871\ldots$

To the nearest cent,

$A=8729.87$