A couple seek a house mortgage on a home valued at $600 000. A bank agrees to su
ID: 3143664 • Letter: A
Question
A couple seek a house mortgage on a home valued at $600 000. A bank agrees to supply this (without mortgage insurance) if they provide a 20% deposit and repay the balance over a 20 year period. (a) They initially contract to pay monthly repayments at a fixed rate of interest of 4.5% adjusted (i.e., compounded) monthly. What are these monthly repayments? The fixed rate operates for 3 years. (b) Find the principal repaid and the interest paid by the end of this 3 year 2 period (i.e. after 36 payments). (c) If this situation obtained for the life of the loan what would be the total amount repaid and the total amount of interest paid?Explanation / Answer
(a)
This is standard EMI calculation problem -
EMI = [P x R x (1+R)^N]/[(1+R)^N-1]
where P stands for the loan amount or principal = 80% x600,000 = $480,000
R is the interest rate per month = 4.5% annual = 4.5%/12 monthly
N is the number of monthly instalments = 240 months
EMI = $3036.72
alternatively you can use the excel formula PMT (R,N,P)
(b)
Total interest paid = 240 EMIs - $480,000 = 240 *3036.72 - 480,000 = $248,812
interest paid in each EMI = $248,812 / 240 = $1036.72
principal paid in each EMI = 3036.72 - 1036.72 = $2000
in 3 years (36 months) interest paid = $1036.72 * 36 = $37,321.81
in 3 years (36 months) principal paid = $2000 * 36 = $72000
(c)
total amount paid we have already calculated in the above part
total amount paid = 240 EMIs = 240 *3036.72 = $728,812
Total interest paid = 240 EMIs - $480,000 = 240 *3036.72 - 480,000 = $248,812
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