Worked solution · Exam FM
This Exam FM sample reference tests Loan Balances and Amortization. The six-month accumulation factor is 1.045, so a month-n cash flow is discounted by 1.045 to the n/6. Payment n is 500 + (n−1)X for n from 1 through 60. This timing and payment expression is choice E.
Independent solution
Setup
The semiannual periodic rate is 9% divided by 2, giving six-month accumulation factor 1.045.
Model
A payment at month n is n/6 half-year periods from origination.
Compute
The first payment is 500, so payment n contains n minus 1 increments.
Answer
This is exactly the equation displayed in choice E.
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Original practice · fully worked
A 20,000 loan is repaid with 36 monthly payments. The first payment is 400 and each later payment is X larger. The annual nominal interest rate is 8% convertible semiannually. Calculate X.
Discounting the 36 base payments and the month-index increment stream using the sixth root of 1.04 gives increment X = 13.43, choice D.
Setup
Convert the six-month factor 1.04 to an equivalent one-month factor.
Model
Separate the payment stream into 400 each month plus X times the index 0 through 35.
Compute
The base-payment present value is 12789.21 and the increment factor is 536.994277, giving X = 13.4280.
Answer
Each payment rises by 13.43, selecting choice D.
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Drill the method: Exam FM Loan Amortization and Balances problems
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