Question

If you buy a house for $300,000 at 3.75% interest, what are your monthly payments for a 30 year conventional loan? If you pay an extra $300 each month, by how much can you reduce the term of your loan?

Answer 1

a). Annuity = [PVA x r] / [1 - (1 + r)^-n]

= [$300,000 x (0.0375/12)] / [1 - {1 + (0.0375/12)}^-(30*12)]

= $937.50 / 0.6748 = $1,389.35

b). New Monthly Payment = $1,389.35 + $300 = $1,689.35

PVA = [Annuity / r] x [1 - (1 + r)^-n]

$300,000 = [$1,689.35 / (0.0375 / 12)] x [1 - {1 + (0.0375 / 12)}^-n]

$300,000 / $540,590.97 = 1 - {1.003125}^-n

{1.003125}^-n = 1 - 0.5549

-n[ln(1.003125] = ln[0.4451]

-n[0.0031] = -0.80968.38

n = 0.8096/0.0031 = 259.47 months

Now, the loan will be repaid in 259.47 months

Hence, It reduces the term of the loan by 100.53 (=360 - 259.47) months, or 8.38 years