Answer:
a. The monthly payment on loan 1 is $76.03.
b. The monthly payment on loan 2 is $411.69.
Explanation:
a. Calculate the monthly payment on loan 1.
To determine the amount of periodic payments, the present value of annuity formula should be used:
[tex]PV=P(\frac{1-(1+r)^{-n} }{r} )[/tex]
Where:
PV= present value
p=periodic payment
i=rate of interest
n=number of periods
We get the data for this exercise:
PV= 3,600 (loan).
p= unknown (we must find this value)
i= 6.6% or 0.066. However, because we need to know the monthly payment, the interest rate should be divided by 12 (0.066 / 12).
n= 4 years and 7 months, that is 55 months.
And we replace in the formula:
[tex]3600=P(\frac{1-(1+\frac{0.066}{12})^{-55} }{\frac{0.066}{12} } )[/tex]
[tex]3600=P(\frac{1-(1+0.055)^{-55} }{0.0055} )[/tex]
[tex]3600=P(\frac{1-(0.7395812268)}{0.0055} )[/tex]
[tex]3600=P(\frac{0.2604187732}{0.0055} )[/tex]
[tex]3600=P(47.348867)[/tex]
Therefore:
[tex]P=\frac{3600}{47.348867}[/tex]
[tex]P=76.03[/tex]
The monthly payment on loan 1 is $76.03.
b. Calculate the monthly payment on loan 2.
We get the data for this exercise:
PV= 11,600 (loan 2).
p= unknown (we must find this value)
i= 7.3% or 0.073. However, because we need to know the monthly payment, the interest rate should be divided by 12 (0.073 / 12).
n= 2 years and 7 months, that is 31 months.
And we replace in the formula:
[tex]11600=P(\frac{1-(1+\frac{0.073}{12})^{-31} }{\frac{0.073}{12} } )[/tex]
[tex]11600=P(\frac{1-(1+0.006083)^{-31} }{0.006083} )[/tex]
[tex]11600=P(\frac{1-(0.8286047296)}{0.006083} )[/tex]
[tex]11600=P(\frac{0.1713952704}{0.006083} )[/tex]
[tex]11600=P(28.1761088936)[/tex]
Therefore:
[tex]P=\frac{11600}{28.1761088936}[/tex]
[tex]P=411.69[/tex]
The monthly payment on loan 2 is $411.69.
