The Colebeck's are purchasing a cottage for $120 000. They have a down payment of $20 000 and borrow the rest at 4.8%/a compounded monthly. If their
monthly payments are $750 determine how long it takes them to pay off the loan?
To determine how long it takes the Colebeck's to pay off the loan, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
where:
FV is the future value of the loan,
P is the monthly payment ($750),
r is the monthly interest rate (4.8% compounded monthly divided by 100, which is 0.048/12),
n is the number of periods (the number of months it takes to pay off the loan).
We need to find the value of n in this equation. Rearranging the formula:
n = log((FV * r + P) / P) / log(1 + r)
Substituting the given values into the formula:
n = log(((120000 - 20000) * (0.048/12) + 750) / 750) / log(1 + (0.048/12))
Now we can calculate this:
n = log(1010/750) / log(1.004)
Using a calculator, we can find the value of n to be approximately 140.12.
Therefore, it would take the Colebeck's approximately 140 months (rounded up to the nearest whole month) to pay off the loan.