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maw [93]
2 years ago
8

Ralph earns $72,000 annually as an architect and is paid semimonthly. Alice also earns $72,000 but she is paid biweekly.

Mathematics
1 answer:
Darya [45]2 years ago
6 0

Step-by-step explanation:

there are 12 months in a year, and therefore 2×12 = 24 "half-months" and therefore semimonthly payments.

that means each paycheck is

72,000 / 24 = $3,000

there are 52 weeks per year.

that means they're are 52/2 = 26 biweekly periods and therefore payments.

each paycheck is therefore

72,000 / 26 = $2,769.23

so, Alice receives 2 more paychecks (26 to 24) in a year.

the difference between the 2 types of payment is

3000 - 2769.23 = $230.77

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Each investment matures in 3 years. The interest compounds annually.
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bearing in mind that 4¾ is simply 4.75.

\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=600\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies A=600(1.05)^3\implies A=694.575 \\\\[-0.35em] ~\dotfill

\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=750\left(1+\frac{0.0475}{1}\right)^{1\cdot 3}\implies A=750(1.0475)^3\implies A\approx 862.032

well, the interest for each is simply A - P

695.575 - 600 = 95.575.

862.032 - 750 = 112.032.

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