It will take approximately 154.33 months to pay off a $51,000 loan at a 12% annual interest rate, with monthly payments of $650, using the amortization formula.
To calculate the time it takes to pay off a loan, we can use the formula for the monthly payment in an amortizing loan:
[tex]\[ M = P \times \frac{r(1+r)^n}{(1+r)^n-1} \][/tex]
where:
- M is the monthly payment,
- P is the loan amount,
- r is the monthly interest rate,
- n is the total number of payments.
First, let's calculate the monthly interest rate (r):
[tex]\[ r = \frac{\text{Annual Rate}}{12 \times 100} \][/tex]
For the given problem:
[tex]\[ r = \frac{12\%}{12 \times 100} = 0.01 \][/tex]
Now, we'll use the formula to calculate the total number of payments (n):
[tex]\[ n = \frac{\log\left(\frac{M}{M - Pr}\right)}{\log(1+r)} \][/tex]
For this problem:
[tex]\[ n = \frac{\log\left(\frac{650}{650 - 51000 \times 0.01}\right)}{\log(1 + 0.01)} \][/tex]
Now, let's calculate this:
[tex]\[ n \approx \frac{\log\left(\frac{650}{650 - 510}\right)}{\log(1.01)} \]\[ n \approx \frac{\log\left(\frac{650}{140}\right)}{\log(1.01)} \]\[ n \approx \frac{\log(4.642857)}{\log(1.01)} \]\[ n \approx \frac{0.6654}{0.00432} \]\[ n \approx 154.33 \][/tex]
So, the result is [tex]\( n \approx 154.33 \)[/tex]. Therefore, it will take approximately 154.33 months to pay off the loan.
Saif is putting tiles on a concrete bird bath. The bird bath is in the shape of a cube with one open face. It takes 4 tiles to cover one square foot of area. Explain how to use a net to find the number of tiles you need to cover the entire outer surface of the bird bath.
Answer: The net is made of 6 squares, but one face is open. I would add the area of 5 squares to get the surface area in square feet. Then, I would multiply the area by 4 to find the number of tiles needed to cover the surface area.
Step-by-step explanation:
How to use a net to find the number of tiles needed to cover the entire outer surface of the bird bath is: Multiply the surface area by 4.
What is Surface area?Surface area can be defined as the number of space that cover the outer surface of a dimensional shape.
Since 4 cover one square foot of area in order to determine the number of tiles to cover the outer surface let the net be 6 squares and the surface area be 5 squares because we have one open face.
Multiply the surface area by the 4 tiles which will give us the number of tiles needed.
Therefore Multiply the surface area by 4.
Learn more about surface area here:https://brainly.com/question/16519513
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