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. (Round your answer to the nearest cent.)

P = 100,000, r = 9.5, t = 23, m = 12

in this example how to find i

To find the periodic payment (R) required to amortize a loan, we can use the formula for the monthly payment of an amortized loan:

R = (P * r / 100) / (1 - (1 + r / (100 * m))^(-m * t))

Here, P = $100,000, r = 9.5%, t = 23 years, and m = 12.

Plugging in the values, we get:

R = (100000 * 9.5 / 100) / (1 - (1 + 9.5 / (100 * 12))^(-12 * 23))

Simplifying this expression, we have:

R = (9500 / 100) / (1 - (1 + 0.095 / 1200)^(-276))

Rounding the values as required, the periodic payment (R) is approximately $835.06.

To find the periodic payment R required to amortize the loan, we can use the formula for calculating the periodic payment for an amortizing loan:

R = (P * (r/m) * (1 + r/m)^(m*t)) / ((1 + r/m)^(m*t) - 1)

Now, let's substitute the given values into the formula:

P = $100,000 (principal amount)
r = 9.5% interest rate (per year)
t = 23 years
m = 12 (compounded monthly)

R = (100,000 * (9.5/100) * (1 + (9.5/100))^(12*23)) / ((1 + (9.5/100))^(12*23) - 1)

Now, let's simplify the formula and calculate the periodic payment:

R = (100,000 * 0.095 * (1 + 0.095)^(276)) / ((1 + 0.095)^(276) - 1)

R = (9,500 * 1.095^(276)) / (1.095^(276) - 1)

Using a calculator, calculating 1.095^(276) = 32.29098189

R = (9,500 * 32.29098189) / (32.29098189 - 1)

R = 306437.328()

Rounded to the nearest cent, the periodic payment R required to amortize the loan is $306,437.33.

i =.095/12 = .00791666...

n = 23x12 = 276

Present value = payment [ 1 - (1+i)^-n]/i
100000= paym[1 - 1.007916667^-276]/.00791666
100000= paym (111.9853...)
payment = 892.97