 Mathematics
14 September, 07:46

# You have just applied, and have been approved for a \$58,000 mortgage. The rate quoted to you by the lender is 6.1% for a 30 year fixed mortgage. Determine how much of your third monthÍs payment goes towards the principal.a.\$56.65c.\$57.22b.\$56.93

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1. 14 September, 08:12
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Here, PV = 58,000, monthly rate = 0.061/12 = 61/12000, n = 30 x 12 = 360 months.

PV = P (1 - (1 + r) ^-n) / r; where P is the periodic payment.

P = PV (r) / (1 - (1 + r) ^-n) = (58000 x 61/12000) / (1 - (1 + 61/12000) ^-360) = (1769/6) / (1 - 0.1612) = 294.8/0.8388 = 351.48

Therefore, the monthly payment is \$351.48

For the first month. Interest due = 58000 (61/12000) = \$294.83

Amount that goes towards the principal = \$351.48 - \$294.83 = \$56.65

Outstanding principal = \$58000 - \$56.65 = \$57,943.35

For the second month. Interest due = \$57,943.35 (61/12000) = \$294.55

Amount that goes towards the principal = \$351.48 - \$294.55 = \$56.93

Outstanding principal = \$57,943.35 - \$56.93 = \$57,886.42

For the third month. Interest due = \$57,886.42 (61/12,000) = \$294.26

Amount that goes towards the principal = \$351.48 - \$294.26 = \$57.22

Therefore, the required amount is \$57.22