Find the periodic payment R required to amortize a loan of P dollars over t yr with interest charged at the rate of r%/year compounded m times a year.
P = 16,000, r = 8, t = 6, m = 6
Here is the formula
A = P * (r(1+r)^n)/((1+r)^n - 1)
Just plug in your numbers
A = Payment/period
P = Principal
r = Rate/period
n = Total of payments or periods
If you post your answer I can check it for you.
i can't figure out what n will be.
im guessing we have the same problem.
n = total payments or periods
Since it is compounded 6 times a year (unusual) n would be,
6 yrs * 6 times a yr = 36
Rate per period, r would be
0.08/6 = 0.0133
To find the periodic payment R required to amortize a loan, you can use the formula for the amortization of a loan:
R = (P * r/100) / (m * (1 - (1 + r/100)^(-m*t)))
Let's substitute the given values into the formula:
P = $16,000
r = 8% (in decimal, r = 0.08)
t = 6 years
m = 6 (compounded 6 times a year)
Now we can calculate the periodic payment R:
R = (16,000 * 0.08/100) / (6 * (1 - (1 + 0.08/100)^(-6*6)))
First, simplify the expression inside the parentheses:
R = (16,000 * 0.08/100) / (6 * (1 - (1 + 0.08/100)^(-36)))
Next, calculate the terms inside the parentheses:
R = (16,000 * 0.08/100) / (6 * (1 - (1 + 0.0008)^(-36)))
Now, simplify further:
R = (16,000 * 0.08/100) / (6 * (1 - (1.0008)^(-36)))
R = (16,000 * 0.08/100) / (6 * (1 - 0.7257))
R = (16,000 * 0.0008) / (6 * 0.2743)
R = 12.8 / 1.6458
Finally, calculate the value of R:
R ≈ $7.78
Therefore, the periodic payment required to amortize the loan is approximately $7.78.