Question

8. Determine the yield-to-maturity at origination for the following mortgages

Mortgage	Monthly Payment ($)	Maturity (In Months)	Amount at origination($)	Yield-to-Maturity
A	500	360	50,000
B	600	360	65,000
C	550	260	62,000
D	550	300	60,000

The correct answers are:

a.

11.63%

b.

10.61%

c.

9.18%

d.

10.11%

I just need to see the work

Answer 1

Case A:

Amount at origination = $50,000
Monthly payment = $500
Period = 360 months

Let monthly YTM be i%

$50,000 = $500 * PVIFA(i%, 360)

Using financial calculator:
N = 360
PV = 50000
PMT = -500
FV = 0

I = 0.969%

Monthly YTM = 0.969%
Annual YTM = 12 * 0.969%
Annual YTM = 11.63%

Case B:

Amount at origination = $65,000
Monthly payment = $600
Period = 360 months

Let monthly YTM be i%

$65,000 = $600 * PVIFA(i%, 360)

Using financial calculator:
N = 360
PV = 65000
PMT = -600
FV = 0

I = 0.884%

Monthly YTM = 0.884%
Annual YTM = 12 * 0.884%
Annual YTM = 10.61%

Case C:

Amount at origination = $62,000
Monthly payment = $550
Period = 260 months

Let monthly YTM be i%

$62,000 = $550 * PVIFA(i%, 260)

Using financial calculator:
N = 260
PV = 62000
PMT = -550
FV = 0

I = 0.765%

Monthly YTM = 0.765%
Annual YTM = 12 * 0.765%
Annual YTM = 9.18%

Case D:

Amount at origination = $60,000
Monthly payment = $550
Period = 300 months

Let monthly YTM be i%

$60,000 = $550 * PVIFA(i%, 300)

Using financial calculator:
N = 300
PV = 60000
PMT = -550
FV = 0

I = 0.843%

Monthly YTM = 0.843%
Annual YTM = 12 * 0.843%
Annual YTM = 10.11%