Final answer:
To calculate the amount of each payment, we can use the formula A = P(1 + r/n)^(nt). Based on the given information, we can rearrange the formula and solve for the annual interest rate. Once we have that, we can calculate the amount of each payment by dividing the final amount by the number of payments per year.
Step-by-step explanation:
To calculate the amount of each payment, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
- A = the final amount
- P = the principal loan amount
- r = the annual interest rate (as a decimal)
- n = the number of times interest is compounded per year
- t = the number of years
Based on the given information, we have:
- P = $1,250,000
- r = the annual interest rate (unknown)
- n = 4 (compounded quarterly)
- t = 1 (one year)
Since we need to find the annual interest rate, we can rearrange the formula:
A/P = (1 + r/n)^(nt)
Substituting the known values:
1 + r/4 = (1 + r)^4
Now, we can solve this equation to find the value of r. Once we have that, we can calculate the amount of each payment by dividing the final amount by the number of payments per year.