Indeed, you can consult online calculators for this problem. But it never hurts to know how to compute and prepare the schedule by hand.
Let’s make some assumptions: The 400,000 loan will be paid in ten equal installments, each installment paid annually with interest of 5%.
First, we need to determine the annual payment with the following formula:
annual payment = face amount / present value of an annuity
The present value of an annuity can be determined in two ways: consulting a present value of an annuity table (found in finance textbooks) or by computing for it with this formula:
present value of an annuity = (1 – (1/(1+i)^n))/i
where n = number of periodic payments, i = interest rate. In our example,
present value of an annuity in 10 years at 5% = (1 – (1/(1+.05)^10))/.05 = 7.7217
Plugging the present value factor into our annual payment formula:
annual payment = 400,000 / 7.7217 = 51801.83
After determining the annual payment, you can prepare the loan amortization schedule as follows:
Make a table with 5 columns. Column headings are as follows from left to right: Year, Annual payment, Interest paid, Principal paid, Balance.
For the first row, put “0″ for Year, empty for annual payment, interest paid, and principal paid, and “400,000″ for Balance.
For the second row, put “1″ for Year; “51801.83″ for annual payment; 400,000 * 0.05 = “20000″ for interest paid; 51801.83 – 20000 = “31801.83″ for principal paid; and 400,000 – 31801.83 = “368198.17″ for Balance.
For the third row, put “2″ for Year; “51801.83″ for annual payment; 368198.17 * 0.05 = “18409.91″ for interest paid; 51801.83 – 18409.91 = “33391.92″ for principal paid, and 368198.17 – 33391.92 = “334806.25″ for balance.
By now, you should have seen the pattern:
1) You add 1 to the previous number for Year
2) “51801.83″ is always the amount for Annual Payment
3) Interest paid is computed by: previous year balance * interest rate. In our example, (previous balance) * 0.05, or 334806.25 * 0.05 = “16740.31″ for Year 4.
4) Principal paid is computed by: annual payment – interest paid. In our example, 51801.83 – [(previous balance) * 0.05], or 51801.83 – 16740.31 = “35061.52″ for Year 4.
5) Balance is computed by: previous balance – principal paid. In our example, previous balance – {51801.83 – [(previous balance) * 0.05], or 334806.25 – 35061.52 = “299744.73″ for Year 4.
Follow the pattern until the last annual payment which is in Year 10.
The last row should be Year 10; 2466.75 for interest paid; 49335.08 for principal paid; and 0 for balance.
If the schedule is computed manually, usually, the balance in the last row is not exactly 0. This does not mean your schedule is wrong. The discrepancy is due to rounding off errors.
I assume the payments will be monthly in equal amounts. Five per cent interest rate is commonly divided by twelve, which is bad mathematics but good business for the lender. Thus .004166666667 would be used.There can be a small difference depending whether it is assumed payment is made at the first or the last of each month. But the basic approach is to divide .05 by 12 as mentioned, then add one and get this raised to the 120th power, possibly using logs or a calculator. I get 1.647009366 . Subtract one. Divide by the monthly interest rate of .004166666 Divide again by the 1.647009366. Get the reciprocal which is .010306551. Multiply by the $400,000.00 principal to get the monthly payment of $4,242.62.
There are a lot of free calculators on the web for this. Go to any real estate company or bank site or try
HRGal | Feb 26, 2010 | Reply
Indeed, you can consult online calculators for this problem. But it never hurts to know how to compute and prepare the schedule by hand.
Let’s make some assumptions: The 400,000 loan will be paid in ten equal installments, each installment paid annually with interest of 5%.
First, we need to determine the annual payment with the following formula:
annual payment = face amount / present value of an annuity
The present value of an annuity can be determined in two ways: consulting a present value of an annuity table (found in finance textbooks) or by computing for it with this formula:
present value of an annuity = (1 – (1/(1+i)^n))/i
where n = number of periodic payments, i = interest rate. In our example,
present value of an annuity in 10 years at 5% = (1 – (1/(1+.05)^10))/.05 = 7.7217
Plugging the present value factor into our annual payment formula:
annual payment = 400,000 / 7.7217 = 51801.83
After determining the annual payment, you can prepare the loan amortization schedule as follows:
Make a table with 5 columns. Column headings are as follows from left to right: Year, Annual payment, Interest paid, Principal paid, Balance.
For the first row, put “0″ for Year, empty for annual payment, interest paid, and principal paid, and “400,000″ for Balance.
For the second row, put “1″ for Year; “51801.83″ for annual payment; 400,000 * 0.05 = “20000″ for interest paid; 51801.83 – 20000 = “31801.83″ for principal paid; and 400,000 – 31801.83 = “368198.17″ for Balance.
For the third row, put “2″ for Year; “51801.83″ for annual payment; 368198.17 * 0.05 = “18409.91″ for interest paid; 51801.83 – 18409.91 = “33391.92″ for principal paid, and 368198.17 – 33391.92 = “334806.25″ for balance.
By now, you should have seen the pattern:
1) You add 1 to the previous number for Year
2) “51801.83″ is always the amount for Annual Payment
3) Interest paid is computed by: previous year balance * interest rate. In our example, (previous balance) * 0.05, or 334806.25 * 0.05 = “16740.31″ for Year 4.
4) Principal paid is computed by: annual payment – interest paid. In our example, 51801.83 – [(previous balance) * 0.05], or 51801.83 – 16740.31 = “35061.52″ for Year 4.
5) Balance is computed by: previous balance – principal paid. In our example, previous balance – {51801.83 – [(previous balance) * 0.05], or 334806.25 – 35061.52 = “299744.73″ for Year 4.
Follow the pattern until the last annual payment which is in Year 10.
The last row should be Year 10; 2466.75 for interest paid; 49335.08 for principal paid; and 0 for balance.
If the schedule is computed manually, usually, the balance in the last row is not exactly 0. This does not mean your schedule is wrong. The discrepancy is due to rounding off errors.
Hope you understood my lengthy explanation!
Good luck with your finances!
blah | Feb 28, 2010 | Reply
I assume the payments will be monthly in equal amounts. Five per cent interest rate is commonly divided by twelve, which is bad mathematics but good business for the lender. Thus .004166666667 would be used.There can be a small difference depending whether it is assumed payment is made at the first or the last of each month. But the basic approach is to divide .05 by 12 as mentioned, then add one and get this raised to the 120th power, possibly using logs or a calculator. I get 1.647009366 . Subtract one. Divide by the monthly interest rate of .004166666 Divide again by the 1.647009366. Get the reciprocal which is .010306551. Multiply by the $400,000.00 principal to get the monthly payment of $4,242.62.
Edward Hyde | Mar 1, 2010 | Reply