Answer:
Monthly payment of Rick will be approximately $ 140.87
Explantion:
GIVEN :
Loan amount [tex]P=\$ 3,200[/tex]
Time duration for loan repayment [tex]n=24 \mathrm{months}[/tex]
Rate of interest [tex]k=4.8 \% \text { per anuum }[/tex]
To find:
Rick's monthly payment will be approximately $140.87
Solution:
Using sum of a finite geometric sequence:
[tex]a=P\left[\frac{[1-r]}{\left[r-r^{n+1}\right]}\right][/tex]
where [tex]r=\frac{1}{1+i}[/tex]
i= monthly interest
but we rate of interest per annum K = 4.8%
now , rate of interest per month, [tex]i=\frac{4.8}{12}=0.4 \%=\frac{0.4}{100}=0.004[/tex]
lets find the value of r
[tex]r=\frac{1}{1+i}[/tex]
[tex]r=\frac{1}{1.004}[/tex]
[tex]r=0.995[/tex] substituting the values,
[tex]a=P\left[\frac{1-r}{r-r^{n+1}}\right][/tex]
[tex]a=3200\left[\frac{1-0.995}{0.995-0.995^{25}}\right][/tex]
[tex]a=3200\left[\frac{0.005}{0.995-0.882}\right][/tex]
[tex]a=3200\left[\frac{0.005}{0.118}\right][/tex]
[tex]a=3200[0.044][/tex]
[tex]a=140.8[/tex]
Result :
Hence the approximate monthly payment of Rick is [tex]$140.87[/tex]
