Answer:
A = $41,250.00 total / 60 for monthly payment = $ 687.5
Step-by-step explanation:
(I = A - P = $8,250.00)
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 5%/100 = 0.05 per year.
Solving our equation:
A = 33000(1 + (0.05 × 5)) = 41250
A = $41,250.00
The total amount accrued, principal plus interest, from simple interest on a principal of $33,000.00 at a rate of 5% per year for 5 years is $41,250.00.
[tex]\bf ~~~~~~~~~~~~ \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right][/tex]
[tex]\bf ~~~~~~ \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\dotfill & \begin{array}{llll} 33000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \stackrel{payments}{\textit{monthly, thus twelve}} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases}[/tex]
[tex]\bf pymt=33000\left[ \cfrac{\frac{0.05}{12}}{1-\left( 1+ \frac{0.05}{12}\right)^{-12\cdot 5}} \right] \\\\\\ pymt=33000\left[ \cfrac{0.0041\overline{6}}{1-\left( 1+ 0.0041\overline{6}\right)^{-12\cdot 5}} \right] \\\\\\ pymt\approx 33000\left[ \cfrac{0.0041\overline{6}}{1-0.779} \right]\implies pymt\approx 33000\left[ \cfrac{0.0041\overline{6}}{0.22} \right] \\\\\\ pymt\approx 33000(0.01887)\implies pymt\approx 622.75[/tex]
