Question

Problem #3: Mort is to pay off a loan of $80,000 with equal payments at the end of every month over 10 years (i.e., 120 months). The ANNUAL effective rate is 4.5%. Mort decides that he can actually manage to pay double the monthly payment each month. How many MONTHS will it take him to pay off the loan? (Include the final month where the last payment will be smaller than all the rest.) Problem #3: Answer in integer number of months. Just Save Submit Problem #3 for Grading Problem #3 Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Your Answer: Your Mark:

Answer 1

First, let's find the monthly payment

Effective monthly rate = (1 + 0.045)^(1/12) - 1

Effective monthly rate = 0.0036748094 = 0.36748094%
$PV = \frac{PMT}{ r } * \left [ 1 - \frac{1}{(1+ r )^{ n }} \right ]$

$80,000 = \frac{PMT}{ 0.0036748094 } * \left [ 1 - \frac{1}{(1+ 0.0036748094 )^{ 120 }} \right ]$

$80,000 = \frac{PMT}{ 0.0036748094 } *0.3560723179$

80,000 = PMT +96.8954520199

$PMT = \frac{80,000}{96.8954520199}$

Now let's find N with PMT = 825.6321461153 * 2 = 1,651.2642922306

PMT = -1,651.2642922306

PV = 80,000

FV = 0

I/Y = 0.36748094

CPT N

N = 53.45009 months

N = 54 months

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