Answer: 8.4 %
Step-by-step explanation:
Since, the monthly payment formula,
![P = \frac{r(PV)}{1-(1+r)^{-n}}](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7Br%28PV%29%7D%7B1-%281%2Br%29%5E%7B-n%7D%7D)
Where, PV is the present value of the loan,
r is the rate per period,
n is the number of periods,
Here, PV = $ 80,000
P = $ 600
n = 12 × 30 = 360
Let r be the annual rate ,
⇒ ![600 = \frac{\frac{r}{12}\times 80,000}{1-(1+\frac{r}{12})^{-360}}](https://tex.z-dn.net/?f=600%20%3D%20%5Cfrac%7B%5Cfrac%7Br%7D%7B12%7D%5Ctimes%2080%2C000%7D%7B1-%281%2B%5Cfrac%7Br%7D%7B12%7D%29%5E%7B-360%7D%7D)
⇒ ![600 = \frac{\frac{80000r}{12}}{1-(1+r/12)^{-360}}](https://tex.z-dn.net/?f=600%20%3D%20%5Cfrac%7B%5Cfrac%7B80000r%7D%7B12%7D%7D%7B1-%281%2Br%2F12%29%5E%7B-360%7D%7D)
⇒ ![600(1-(1+\frac{r}{12})^{-360}) = \frac{80,000r}{12}](https://tex.z-dn.net/?f=600%281-%281%2B%5Cfrac%7Br%7D%7B12%7D%29%5E%7B-360%7D%29%20%3D%20%5Cfrac%7B80%2C000r%7D%7B12%7D)
⇒ ![r = 0.082](https://tex.z-dn.net/?f=r%20%3D%200.082)
Thus, the annual rate of interest = 0.082 = 8.2 %