evaluate the amortization formula m= p(r/n)/1-(1+r/n)^nt for the variables p,r, and t (respectively). Assume n=12 (Round your answer to nearest cent.) $150,000;6%;15 yr
To evaluate the amortization formula, we need to substitute the values of the variables p, r, and t into the formula and calculate the result. In this case, we have:
Principal amount (p) = $150,000
Annual interest rate (r) = 6%
Loan term in years (t) = 15
Let's begin by converting the annual interest rate to a monthly interest rate, since the formula uses monthly periods. We do this by dividing the annual interest rate by the number of months in a year:
Monthly interest rate = Annual interest rate / Number of periods in a year
= 6% / 12
= 0.06 / 12
= 0.005
Now, let's substitute the values into the amortization formula:
m = p(r/n) / (1 - (1+r/n)^(nt))
where:
m = monthly payment
p = principal amount
r = interest rate per period
n = number of periods per year
t = loan term in years
Substituting the values:
m = $150,000(0.005/12) / (1 - (1+0.005/12)^(12*15))
Now, let's simplify and solve this equation. Remember to round the answer to the nearest cent as mentioned:
m = $625.00
Therefore, the monthly payment (m) for a $150,000 loan at 6% interest over a 15-year term, using monthly compounding, is $625.00.