Richard said:
I want to set up a loan, lets say for 100,000. The payments are interest
only, payable and compounded monthly. the principal of the loan is due
on 60 months.
The answer might depend on the your country. The following applies to the
US, according to Reg Z ("Truth in Lending").
(Note: This applies to a regulated lender. For a private loan, anything
is possible.)
If the annual interest rate is 5%, the monthly rate is 5%/12, and the
interest-only monthly payment is 100000*5%/12.
what if i wanted to then amortorize the principal at the end of the 5
year
period for another 3 years after the interest only term. The interest is
compounded daily and payable over 36 months
This is a little trickier because of the requirement to compound interest
daily.
The "principal at the end of the [interest-only] 5-year period" is the
original amount of the loan, of course.
If the annual interest rate is still 5%, the daily rate is 5%/365 (even in
a leap year). Since the interest is compounded daily, the amount of
interest paid each month is typically (payment in arrears):
previousBalance*(1+5%/365)^(d2-d1) - previousBalance
where d1 and d2 are the previous and current payment due dates.
Typically, d1 and d2 are the same of day of each month. If the first
payment is due on the 31st, the last day of each month is used. If the
first payment is due on the 29th or 30th, the last day of Feb is used.
The amount of principal paid is: payment - interestPaid
The new balance is: previousBalance + interestPaid - payment; or
equivalently: previousBalance - principalPaid.
There is no regulation for how the monthly payment is determined when the
interest is compounded daily and paid monthly. I would determine regular
monthly payment this way:
ROUND(PMT((1+5%/365)^(365/12)-1,12,-100000),2)
But there are other reasonable ways to formulate that. Also note that the
amount of last payment might be different due to real-world rounding and
the variable amount of interest each month. So I would compute the last
payment this way:
MIN(regularPayment, ROUND(previousBalance*(1+5%/365)^(d2-d1),2))
(You can use the same formula for all periodic payments, if you prefer.)
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