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:
![PV=P(\frac{1-(1+r)^{-n} }{r} )](https://tex.z-dn.net/?f=PV%3DP%28%5Cfrac%7B1-%281%2Br%29%5E%7B-n%7D%20%7D%7Br%7D%20%29)
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:
![3600=P(\frac{1-(1+\frac{0.066}{12})^{-55} }{\frac{0.066}{12} } )](https://tex.z-dn.net/?f=3600%3DP%28%5Cfrac%7B1-%281%2B%5Cfrac%7B0.066%7D%7B12%7D%29%5E%7B-55%7D%20%7D%7B%5Cfrac%7B0.066%7D%7B12%7D%20%7D%20%29)
![3600=P(\frac{1-(1+0.055)^{-55} }{0.0055} )](https://tex.z-dn.net/?f=3600%3DP%28%5Cfrac%7B1-%281%2B0.055%29%5E%7B-55%7D%20%7D%7B0.0055%7D%20%29)
![3600=P(\frac{1-(0.7395812268)}{0.0055} )](https://tex.z-dn.net/?f=3600%3DP%28%5Cfrac%7B1-%280.7395812268%29%7D%7B0.0055%7D%20%29)
![3600=P(\frac{0.2604187732}{0.0055} )](https://tex.z-dn.net/?f=3600%3DP%28%5Cfrac%7B0.2604187732%7D%7B0.0055%7D%20%29)
![3600=P(47.348867)](https://tex.z-dn.net/?f=3600%3DP%2847.348867%29)
Therefore:
![P=\frac{3600}{47.348867}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B3600%7D%7B47.348867%7D)
![P=76.03](https://tex.z-dn.net/?f=P%3D76.03)
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:
![11600=P(\frac{1-(1+\frac{0.073}{12})^{-31} }{\frac{0.073}{12} } )](https://tex.z-dn.net/?f=11600%3DP%28%5Cfrac%7B1-%281%2B%5Cfrac%7B0.073%7D%7B12%7D%29%5E%7B-31%7D%20%7D%7B%5Cfrac%7B0.073%7D%7B12%7D%20%7D%20%29)
![11600=P(\frac{1-(1+0.006083)^{-31} }{0.006083} )](https://tex.z-dn.net/?f=11600%3DP%28%5Cfrac%7B1-%281%2B0.006083%29%5E%7B-31%7D%20%7D%7B0.006083%7D%20%29)
![11600=P(\frac{1-(0.8286047296)}{0.006083} )](https://tex.z-dn.net/?f=11600%3DP%28%5Cfrac%7B1-%280.8286047296%29%7D%7B0.006083%7D%20%29)
![11600=P(\frac{0.1713952704}{0.006083} )](https://tex.z-dn.net/?f=11600%3DP%28%5Cfrac%7B0.1713952704%7D%7B0.006083%7D%20%29)
![11600=P(28.1761088936)](https://tex.z-dn.net/?f=11600%3DP%2828.1761088936%29)
Therefore:
![P=\frac{11600}{28.1761088936}](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B11600%7D%7B28.1761088936%7D)
![P=411.69](https://tex.z-dn.net/?f=P%3D411.69)
The monthly payment on loan 2 is $411.69.