Thread: solve for interest rate

Hello, I am looking for the formula to solve for interest rate. I know to following:

Initial Loan Amount: $100,000
Term (years or months): 30/360
Monthly payment: $536.82
twelve pay periods per year

correct answer 5.50%

Thank you

What formula(s) did they give you for this homework exercise? Perhaps we can work from there.

Problem: Initial Loan Amount: $100,000
Term (years or months): 30/360
Monthly payment: $536.82
twelve pay periods per year
correct answer 5.50%
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Solution:

Let:
r = the yearly nominal interest rate. t = the number of years. m = the number of periods per year. i = the interest rate per period. n = the number of periods. Note:
n = tm Also let:
P = the principal (or present value). R = the periodic payment in an annuity (the amortized payment).
Also: .


P = $100,000.00,
t = 30 year,
R = $536.82
m = 12 periods in 1 year,
i = r/m = r/12,
n = tm = 30(12) = 360

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using this Formula: .

100000 = (536.82)(1 - (1/(1 + r/12)^360))/(r/12),

100000/536.82 = (12/r)[1 - (1 + (r/12))^-360]

(100000/536.82)(r/12) = 1 - (1 + (r/12))^-360

(1 + (r/12))^-360 = 1 - (100000/536.82)(r/12) = 1 - 15.524r

1 = (1 - 15.524r)(1 + (r/12))^360,

wow! what a big number, i will use substititution.

The only thing that equals the left hand side is when r = 0.04999999 is used at the right hand side of the equation.

so, r = 0.049999 = 0.05 = 5% = nominal rate of interest.

effective rate of interest = (1 + 0.05/12)^12 - 1 = 1.05116 - 1 = 0.05116 = 5.116%

My answer differs greatly. . . . i can not find where is my mistake.