Question

a. If Dave had borrowed $480 for one year at an APR of 6 percent, compounded monthly, what would have been his monthly loan payment?

b. What would have been the breakdown between interest and principal of the fifth payment?

Answer 1

Formula for EMI is
EMI = [P x R x (1+R)N]/[(1+R)N -1]
where,
P = Loan amount or principal
R = interest rate per month
N = number of monthly installments.

R = 6 / 12 = 0.5% per month compounding monthly
N = 1 * 12 = 12 Months

EMI = [$480 * 0.005 * (1 + 0.005)12]/ [(1 + 0.005)12 - 1]
        = [$480 * 0.005 * (1.005)12]/ [(1.005)12 - 1]
        = [$480 * 0.005 * 1.0617]/ [1.0617 - 1]
        = [$2.5480]/ 0.0617
        = 41.31
       

Calculation of the interest and principal of the 5th payment :


Interest amount of 5th installment = 1.62 (rounded off)
Principal amount of 5th installment = 39.70 (rounded off)