Question

1. We expect a cash flow of $80,000 in 85 days. Given a discount rate of 5.75% per year compounded semi-annually, what is the present value of this cash flow?

2. You have just negotiated a 5-year mortgage on $400,000 amortized over 25 years at a rate of 3.5%. After 5 years assume that the mortgage rate remains the same, but you increase the payments by 500 dollars per month, in how many periods (months) will you be able to pay the whole amount. (Hint: Canadian banks quote mortgage rates as a rate per year compounded semi-annually).

Answer 1

1. CF = 80,000

n = 85 days

Effective daily rate, r = (1 + 0.0575/2)^(2/365) - 1

r = 0.0001553242424

PV = CF/(1 + r)^n

PV = 80,000/(1 + 0.0001553242424)^85

PV = 80,000/1.0132890604

PV = $78,950.8178134477

2. Step 1: Find original monthly payment

Effective monthly rate, r = (1 + 0.035/2)^(1/6) - 1

r = 0.002895623966

Number of monthly payments, n = 25 * 12 = 300

PV = 400,000

This is the original monthly payment

Step 2: We will find the loan outstanding at the end of 5 years

Number of payments remaining after 5 years, n = (25 - 20) * 12

n = 240

PMT = 1,997.0813293829

r = 0.002895623966

Step 3: We will find the number of months required to payoff this loan outstanding with additional payment of $500 per month

PMT = 1,997.0813293829 + 500

PMT = 2497.0813293829

PV = -345119.927872556

FV = 0

I/Y = 0.2895623966

CPT N

N = 176.7848517

N is close to 177 months

The number of months required to payoff the whole amount = 60 + 177

The number of months required to payoff the whole amount = 237 months

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