Question

a)

Mariah borrowed $50,000 for 30 years at 11.2 percent compounded semiannually. How much of payment 36 will go towards paying off principal?

$877.79

$745.42

$831.24

$787.16 b) Chris borrowed $52,000 for 25 years at 5.4 percent compounded monthly. What will the ending balance be after Chris has made one year of payments? $51,074.87 $50,988.48 $50,901.70

Answer 1

Answer a.

Amount borrowed = $50,000
Annual Interest Rate = 11.2%
Semiannual Interest Rate = 5.6% (11.2%/2)
Semiannual Period = 60 (30 years)

Semiannual Payment * PVIFA(5.6%, 60) = $50,000
Semiannual Payment * (1 - (1/1.056)^60) / 0.056 = $50,000
Semiannual Payment * 17.1780 = $50,000
Semiannual Payment = $2,910.70

Balance after 35 payments = $2,910.70 * PVIFA(5.60%, 25)
Balance after 35 payments = $2,910.70 * (1 - (1/1.056)^25) / 0.056
Balance after 35 payments = $2,910.70 * 13.2840
Balance after 35 payments = $38,665.73

Balance after 36 payments = $2,910.70 * PVIFA(5.60%, 24)
Balance after 36 payments = $2,910.70 * (1 - (1/1.056)^24) / 0.056
Balance after 36 payments = $2,910.70 * 13.0279
Balance after 36 payments = $37,920.31

Principal repaid in payment 36 = Balance after 35 payments - Balance after 36 payments
Principal repaid in payment 36 = $38,665.73 - $37,920.31
Principal repaid in payment 36 = $745.42

Answer b.

Amount borrowed = $52,000
Annual Interest Rate = 5.40%
Monthly Interest Rate = 0.45% (5.4%/12)
Period = 300 months

Monthly Payment * PVIFA(0.45%, 300) = $52,000
Monthly Payment * (1 - (1/1.0045)^300) / 0.0045 = $52,000
Monthly Payment * 164.43855 = $52,000
Monthly Payment = $316.23

Balance after 12 payments = $316.23 * PVIFA(0.45%, 288)
Balance after 12 payments = $316.23 * (1 - (1/1.0045)^288) / 0.0045
Balance after 12 payments = $316.23 * 161.23983
Balance after 12 payments = $50,988.48