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Homework answers / question archive / years and months (from 0 to 11 months)
years and months (from 0 to 11 months). A mortgage of $122,000 is to be repaid by making payments of $1015 at the end of each month. If interest is 3.02% per annum compounded annually, what is the term of the mortgage? State your answer i The term of the mortgage is year(s) and month(s).
We need to find the term of the mortgage given the following:
Mortgage amount, PV = 122,000
Monthly payment, PMT = -1015
Negative cash flow indicates cash outflow.
Annual interest rate = 3.02%
Effective monthly interest rate = (1 + Annual interest rate)^(1/m) - 1
Where,
m = Number of months in a year
m = 12
Effective monthly interest rate = (1 + 3.02%)^(1/12) - 1
Effective monthly interest rate = 1.0024824895 - 1
Effective monthly interest rate = 0.0024824895
Effective monthly interest rate = 0.24824895%
I/Y = 0.24824895
So, we have
PV = 122,000
PMT = 1015
I/Y = 0.24824895
FV = 0
CPT N
N = 142.9268 months
We divide by 12 to get the number of years
N = 142.9268/12 = 11.9105666667 Years
Or 11 Years and 0.9105666667 * 12 Months
Or 11 Years and 11 Months
The term of the mortgage is 11 years and 11 months
