Question

You wish to buy a house for ​$295987. The bank offers you a mortgage loan of 3.7​% for 25 years. How much will your monthly payments​ be? ​(Round to the nearest​ cent) After the life of the​ loan, how much did you really spend for your​ home? ​(Round to the nearest​ cent)

Answer 1

Monthly payments: $2446.92

Total expenditure: $734,076.88

Explanation:

As the compounding frequency is not stated, it is supposed to be annualy.

The total accumulated value T, including the loan L and the interest is given by the formula

`T=L(1+(r)/(n))^(nt)`

where

L = Amount of the loan

r = nominal interest per year. In this case, 0.037

n = compounding frequency, in this case 1 year

t = the length of time the interest is applied. In this case, 25 years.

The total amount after 25 years will be

`T=295987(1+0.037)^(25)=295987(1.037)^(25)=734076.88`

There are 25 times 12 = 300 months in 25 years, so the monthly payments would be

`(734076.88)/(300)=\$2446.92`

After the life of the loan, if there are no additional commissions or expenditures, you would have spent the amount of the loan plus interest, that is to say, the amount T previously computed

$734076.88