2Assume you borrowed $250,000 for a home, at 4.5% interest for 30 years,to be pa

Question

2Assume you borrowed $250,000 for a home, at 4.5% interest for 30 years,to be paid back in monthly installments over the next 30 years?a) How much would your monthly payment be?b) How much interest would you pay over the 30 years in total?c) If you pay back the loan in equal installments over the next15 years instead of 30 years how much would your monthly payment be?d) If you pay back the loan in equal installments over the next15 years instead of 30 years how much interest you pay over the 15 years?

Explanation / Answer

Formula to calculate Monthly installment = [P x R x (1+R)^N]/[(1+R)^N-1]. Here P stands for the loan amount (i.e. $250,000), R is the interest rate per month (i.e. 4.5%/12) , and N is the number of monthly instalments (i.e. 30*12=360 for 30 year term and 15*12=180 for 15 year term).

We will get following results based on above formula -

a) Monthly payment = [250000*(4.5%/12)*(1+(4.5%/12)^360)]/[(1+(4.5%/12)^360)-1] = $1,266.71

b) Total Interest payment over 30 year period = total payments over the period-principal loan amount = $1,266.71*360-250000=206,016

c)Monthly payment = [250000*(4.5%/12)*(1+(4.5%/12)^180)]/[(1+(4.5%/12)^180)-1] = $1,912.48

b) Total Interest payment over 15 year period = total payments over the period-principal loan amount = $1,912.48*180-250000=92,246

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