Suppose you wish to borrow 635.08 dollars today from a bank which charges interest at a rate of 4.14% per month. You promise to pay the loan back over 14 years by making the same payment each month (starting with month 1). What will be your montly payment?
To calculate the monthly payment for a loan with a fixed interest rate and equal monthly payments, you can use the formula for the monthly payment of an amortizing loan.
The formula for the monthly payment, also known as the loan payment or annuity payment, is given by:
P = (Pv * r) / (1 - (1 + r)^-n)
Where:
P = Monthly payment
Pv = Present value or loan amount
r = Monthly interest rate
n = Total number of months
Given:
Pv = $635.08
r = 4.14% per month expressed as a decimal (0.0414)
n = 14 years = 14 * 12 = 168 months
Let's plug in these values into the formula to calculate the monthly payment:
P = (635.08 * 0.0414) / (1 - (1 + 0.0414)^-168)
Now, we can simplify the formula and solve for P:
P = (26.346312) / (1 - (1.0414)^-168)
P = 26.346312 / 0.3548478103
P ≈ $74.18
Therefore, your monthly payment for a loan of $635.08 over 14 years at an interest rate of 4.14% per month would be approximately $74.18.