# Amortization 360 vs 365 Days

#### johndrew

##### Board Regular
I have a loan for \$755,812 at 6.0% for 5 years. I put this in as pmt and got a montly payment of \$14,611.98. The bank has a payment of \$14,644.10.

I asked the bank why the difference and they said it was the difference between 360 days vs 365.

How do I calculate it to get their montly payment and make an amortization schedule with interest and principal?

Thanks

### Excel Facts

What is =ROMAN(40) in Excel?
The Roman numeral for 40 is XL. Bill "MrExcel" Jelen's 40th book was called MrExcel XL.

#### Mexcel

##### New Member
Your banks payment is equivalent to an AER of 6.264%. Now I can get pretty close to your banks payment with ((1+6%/360)^(365/12)-1) as monthly interest rate on the outstanding balance. This is of course a rediculous way of calculating interest. A normal APR is also rediculous but in that case it should have been ((1+6%/12)^1-1) for the monthly rate. Banks wil try to explain to you this is absolutely necessary. Except when you loan money to them. Then on your savings account you always get the qouted rate as effective annual rate.

#### Richard Schollar

##### MrExcel MVP
Hello John

I can't get the bank's number exactly but this is how I would approach it:

Excel Workbook
ABCDE
1Initial loan755,812.00
2Interest rate6%
3BasisA360
4Term5 years
5Period12 (monthly)
6Type0
7
8To convert A360 to A3656.0833%
9
10PMT on this basis-14,641.27
11
12
13PeriodPaymentInterestCapitalOutstanding
140-755,812.00
15114,641.273,831.5510,809.72-745,002.28
16214,641.273,776.7510,864.52-734,137.76
17314,641.273,721.6710,919.60-723,218.16
18414,641.273,666.3110,974.95-712,243.21
19514,641.273,610.6811,030.59-701,212.62
20614,641.273,554.7611,086.51-690,126.11
21714,641.273,498.5611,142.71-678,983.39
22814,641.273,442.0711,199.20-667,784.19
23914,641.273,385.2911,255.97-656,528.22
241014,641.273,328.2311,313.03-645,215.19
251114,641.273,270.8811,370.39-633,844.80
261214,641.273,213.2411,428.03-622,416.77
271314,641.273,155.3111,485.96-610,930.81
281414,641.273,097.0811,544.19-599,386.62
291514,641.273,038.5611,602.71-587,783.91
301614,641.272,979.7411,661.53-576,122.38
311714,641.272,920.6211,720.65-564,401.73
321814,641.272,861.2011,780.06-552,621.67
331914,641.272,801.4811,839.78-540,781.89
342014,641.272,741.4611,899.80-528,882.08
352114,641.272,681.1411,960.13-516,921.95
362214,641.272,620.5112,020.76-504,901.19
372314,641.272,559.5712,081.70-492,819.49
382414,641.272,498.3212,142.95-480,676.54
392514,641.272,436.7612,204.51-468,472.04
402614,641.272,374.8912,266.38-456,205.66
412714,641.272,312.7112,328.56-443,877.10
422814,641.272,250.2112,391.06-431,486.05
432914,641.272,187.3912,453.87-419,032.17
443014,641.272,124.2612,517.01-406,515.16
453114,641.272,060.8112,580.46-393,934.70
463214,641.271,997.0312,644.24-381,290.46
473314,641.271,932.9312,708.34-368,582.13
483414,641.271,868.5112,772.76-355,809.37
493514,641.271,803.7612,837.51-342,971.85
503614,641.271,738.6812,902.59-330,069.26
513714,641.271,673.2712,968.00-317,101.26
523814,641.271,607.5313,033.74-304,067.52
533914,641.271,541.4513,099.81-290,967.71
544014,641.271,475.0413,166.22-277,801.48
554114,641.271,408.3013,232.97-264,568.51
564214,641.271,341.2213,300.05-251,268.46
574314,641.271,273.7913,367.48-237,900.98
584414,641.271,206.0313,435.24-224,465.74
594514,641.271,137.9213,503.35-210,962.39
604614,641.271,069.4613,571.81-197,390.58
614714,641.271,000.6613,640.61-183,749.98
624814,641.27931.5113,709.76-170,040.22
634914,641.27862.0113,779.26-156,260.96
645014,641.27792.1613,849.11-142,411.85
655114,641.27721.9513,919.32-128,492.53
665214,641.27651.3913,989.88-114,502.64
675314,641.27580.4614,060.80-100,441.84
685414,641.27509.1814,132.08-86,309.76
695514,641.27437.5414,203.73-72,106.03
705614,641.27365.5414,275.73-57,830.30
715714,641.27293.1714,348.10-43,482.20
725814,641.27220.4314,420.84-29,061.36
735914,641.27147.3214,493.94-14,567.42
746014,641.2773.8514,567.420.00
Sheet1
Excel 2003
Cell Formulas
RangeFormula
B8=B2*365/360
B10=PMT(B8/12,B4*B5,B1,0,B6)
B15=-\$B\$10
E14=-B1
E15=E14+D15
C15=E14*\$B\$8/12*-1
D15=B15-C15

#### drpoyner

##### New Member
Can you help me with the formulas on a actual/365 (fixed) loan amortization? Thanks. \$20,000,000 loan; 3.25% interest rate; 25 year amortization; monthly payments

Here you go:

#### drpoyner

##### New Member
Thanks. What is the difference between that formula and one used 30/360? I guess I am struggling with the correct formula to use for the various amortization schedules. I appreciate your help.

##### Board Regular
If they are doing an actual day (365 days per year) calculation then it is very possible that they are assuming actual days for each month rather than a month being 1/12 of a year. In that case the interest would be daily and the days between each payment would vary depending upon the number of days in the month. This is a common practice for consumer loans as opposed to mortgages. If that is the case you have to amortize the loan and iterate on the payment rather than solving it in closed form.

#### japes

##### New Member
Can someone help me figure out a mortgage payment formula in excel using the PMT function? I have a \$11,000,000 loan, interest rate is 3.99%, amortization is 25 years. The bank is telling me the monthly payment is \$58,360.23, but I cannot get the same result using the pmt calculation. Any help is appreciated...

##### Board Regular
I get \$58,001.33 both with PMT function and with my HP 12C financial calculator.

#### japes

##### New Member
I get \$58,001.33 both with PMT function and with my HP 12C financial calculator.
Thanks. I get this as well, but the bank says the payment is \$58,360.23. I was hoping someone can show me how they are arriving at that number.

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