麦德琳（Madeline）将 $6 000 存入 3 个月的定期存款，该存款支付单利。如果她在 3 个月结束时共收到 $6 013.50，那么年利率是多少？ 答案 ...% 另一家银行提供 0.6% 的年利率，按月复利。如果麦德琳把这 $6 000 存入这家银行，在 3 个月结束时，她收到的总金额（精确到元）是多少？ 答案 $...

1. Find the simple interest earned in 3 months.

Interest earned
$= 6013.50 - 6000 = 13.50$
So the simple interest for 3 months is $13.50.

2. Convert the 3-month simple interest to a rate per annum.

For 3 months,
$\text{rate} = \frac{13.50}{6000} \times 100\% = 0.225\%$
Since 3 months is $\frac{1}{4}$ of a year,
$\text{rate per annum} = 0.225\% \times 4 = 0.9\%$

1. Find the monthly interest rate and corresponding multiplier.

Monthly interest rate
$=\frac{0.6\%}{12}=0.05\%$
Monthly multiplier
$=1+\frac{0.05}{100}=1.0005$

2. Calculate the amount after 3 monthly compoundings and round to the nearest dollar.

Amount after 3 months
$=6000(1.0005)^3$
$=6009.00300075\ldots$
Correct to the nearest dollar,
$\$6009$