Question

A mortgage requires payments of $1,000.00 at the end of every month for 25 years. If interest is 6% compounded semi-annually, calculate the principal of the loan. Select one: O a. $300,000 b. $33,328.64 O c. $155,206.86 O d. $156,297.23 e. $46,188.41

Answer 1

The principal amount of the loan can be calculated by finding the present value of the payments.

$PV = \frac{PMT}{r} * \left [ 1 - \frac{1}{(1+r)^{n}} \right ]$

n = 25 * 12 = 300

r = (1 + 0.06/2)^(1/6) -1 = 0.004938622031

$PV = \frac{1,000}{0.004938622031} * \left [ 1 - \frac{1}{(1+0.004938622031)^{300}} \right ]$

$PV = 202,485.631360923 * 0.7718929202$

$PV = \$156,297.23$

Option d is correct.

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