Find the periodic payment R required to amortize a loan of P dollars over t years with interest charged at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)
P = 11,000, r = 4, t = 4, m = 2
i = .04/2 = .02
n = 4*2 = 8
PV = 11000
paym = ?
11000 = paym(1 - 1.02^-8)/.02
solve for paym, let me know what you got.
To find the periodic payment, R, required to amortize a loan, we can use the formula for the periodic payment in an amortization schedule. The formula is given by:
R = (P * (r/m) * (1 + r/m)^(m*t)) / ((1 + r/m)^(m*t) - 1)
where:
P is the principal amount (loan amount),
r is the annual interest rate as a percentage,
t is the number of years,
m is the number of times the interest is compounded per year.
Given:
P = $11,000
r = 4% (or 0.04 as a decimal)
t = 4 years
m = 2 times per year
Substituting the given values into the formula, we have:
R = (11000 * (0.04/2) * (1 + 0.04/2)^(2*4)) / ((1 + 0.04/2)^(2*4) - 1)
Calculating this expression step by step:
Step 1: Calculate the values inside the parentheses:
(0.04/2) = 0.02
(1 + 0.04/2) = 1.02
(2*4) = 8
Step 2: Calculate the values inside the square brackets:
(1.02^8) = 1.17161952
Step 3: Calculate the denominator of the formula:
((1.02^8) - 1) = 0.17161952
Step 4: Calculate the final result:
(11000 * 0.02 * 1.17161952) / 0.17161952
Step 5: Round the result to the nearest cent.
By performing these calculations, we find that the periodic payment, R, required to amortize the loan is approximately $3,303.35.