math

A $15,000 debt is to be amortized in 12 equal semiannual payments at 5.5% interest per half-year on the unpaid balance. Construct an amortization table to determine the unpaid balance after two payments have been made. Round values in the table to the nearest cent.

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  1. The formula for calculating the payment amount is shown below.

    A = P * ((r(1+r)^n)/(((1+r)^n)-1)
    Simple Amortization Calculation Formula
    where

    A = payment Amount per period
    P = initial Principal (loan amount)
    r = interest rate per period
    n = total number of payments or periods

    A = 15000 * ((0.055(1.055)^12)/(((1.055)^12) - 1)

    A = 15000 * ((0.055*1.9012)/.9012)

    A = 1,740.44

    Year 1, first payment: $1740.44 Interest paid = balance * 0.055 = $15000*.055 = $825
    Principal paid = payment - interest = $ 1740.44 - 825 = 915.00
    Balance = 15000 - 915 = 14085

    Year 1, 2nd payment: $1740.44
    Interest paid = balance * 0.055 = $14085*.055 = $774.68
    Principal paid = payment - interest = $ 1740.44 - 774.68 = 965.76
    Balance = 14085 - 965.76 = 13119

    13119 is the unpaid balance after 2 payments.

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  2. A debt of $5000 is to be amortized with 6 equal semiannual payments. If the interest rate is 9%, compounded semiannually, what is the size of each payment

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