A $15,000 debt is to be amortized in 12 equal semiannual payments at an annual interest rate of 11% on the unpaid balance. Construct an amortization table to determine the unpaid balance after two payments have been made.
first you need the monthly payment.
i = .11/12= .00916666..
n = 12
Paym (1 - 1.0091666..^-12)/.009166.. = 15000
paym = 1325.72
Here are my titles to the amortization table ( they will not line up niceley)
Time - payment - interest - repayment - balance
now -- 0.00 -- 0.00 -- 0.00 -- 15000.00
1 -- 137.50 -- 1188.22 -- 13811.78
2 -- 126.61 -- 1199.11 -- 12612.67
....
To construct an amortization table, we need to calculate the payment amount and unpaid balance after each payment. The payment amount for an amortized loan can be calculated using the formula for the present value of an annuity:
PMT = R * PVIFA(i, n)
Where:
PMT = Payment amount
R = Annual interest rate
PVIFA = Present Value Interest Factor Annuity
i = Interest rate per period
n = Number of periods
In this case, since the payments are semiannual, we need to divide the annual interest rate by 2 (i = 11% / 2 = 0.055) and multiply the number of periods by 2 (n = 12 * 2 = 24). The present value factor can be looked up in a present value interest factor of annuity table or calculated using the formula:
PVIFA = (1 - (1 + i)^(-n)) / i
Using the given values, we can calculate the payment amount (PMT):
PMT = R * PVIFA(i, n)
= 0.055 * ((1 - (1 + 0.055)^(-24)) / 0.055)
≈ $902.51
Now, let's construct the amortization table to determine the unpaid balance after two payments.
Payment | Payment Amount | Interest | Principal | Unpaid Balance
--------------------------------------------------------------------
1 | $902.51 | $825.00 | $77.51 | $14,922.49
2 | $902.51 | $818.07 | $84.44 | $14,838.05
To calculate the interest for each payment, we multiply the unpaid balance by half of the annual interest rate. For the principal, we subtract the interest from the payment amount. And to calculate the unpaid balance, we subtract the principal from the previous unpaid balance.
In the table, after two payments, the unpaid balance is $14,838.05.