CFA Level IQuantitative MethodsMedium
A homebuyer takes out a $200,000 mortgage at a 6% annual interest rate, compounded monthly, to be repaid over 30 years (360 monthly payments) in equal installments. What is the amount of principal repaid in the very first monthly payment?
- A$1,199.10
- B$199.10
- C$200.90
- D$1,000.00
Show answer & explanationAnswer & explanation
Correct answer: B. $199.10
Monthly rate = 6%/12 = 0.5%. Monthly payment = PV×r/(1-(1+r)^-n) = 200,000×0.005/(1-1.005^-360) ≈ 1,000/0.8340 ≈ $1,199.10. First month's interest = 200,000×0.005 = $1,000.00. Principal repaid = 1,199.10 − 1,000.00 = $199.10.
Why the other options are wrong
- A. This is the total monthly payment, not just the principal component.
- C. Close but incorrect due to a rounding/calculation error in the payment amount.
- D. This is the interest portion, not principal.
Loan Amortization
Each fixed loan payment consists of an interest portion (based on the remaining balance) and a principal portion; early payments are interest-heavy.
- Interest portion = beginning balance × periodic rate
- Principal portion = total payment − interest portion
- Principal portion grows over the life of the loan as balance declines
Memory trick: Early payments feed the bank's interest, later payments shrink your debt