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TFSA broken out into quarters
September 14, 2019
2:03 pm
Winnie
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CHUCK21 said
SORRY BUT I'M STILL BEFUDDLED. PLEASE CHECK MY MATH. LETS ASSUME HUBERTS RATE TO BE 2.5% FOR JAN, FEB. & MAR.
2.6% FOR APR, MAY & JUNE
2.7% FOR JUL, AUG. & SEPT. AND
2.8% FOR OCT, NOV. & DEC.
THEN WITH A 60,000 INVESTMENT THE FIRST PAYMENT WOULD BE FOR 90 DAYS = $369.86, THE SECOND PAYMENT ON 60,369.86 FOR 91 DAYS = $391.33, THE THIRD PAYMENT ON 61,761.19 FOR 92 DAYS = $420.31 AND THE LAST QUARTERLY PAYMENT ON 62,181.50 FOR 92 DAYS = $438.85 FOR A TOTAL OF 62,620.35.
IF I TAKE THE MID POINT OF THE INTEREST PAYMENTS I GET 2.65 THEREFORE I GET 60,000 X 2.65 = 61,500.00.
WHAT AM I DOING WRONG?
PLEASE EXCUSE THE CAPS AGAIN.  

$60,000 investment:
The first payment for 90 days = $369.86
The second payment on 60,369.86 for 91 days = $391.33
The third payment on 60,761.19 for 92 days = $413.51
The last payment on 61,174.70 for 92 days = $431.74
Maturity $61,606.44.

$60,000 x 2.65% = $1,590 + $60,000 = $61,590.

$61,606.44 - $61,590 = $16.44

You will get that $16.44 extra, because quarterly interest actually includes compound interest.

September 14, 2019
2:59 pm
Norman1
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I GET SLIGHTLY DIFFERENT AMOUNTS FOR THE LAST TWO QUARTERS. BUT, I THINK WE HAVE THE RIGHT IDEA:

First Day Last Day Days Rate Start Interest
02-Jan-2019 01-Apr-2019 90 2.50% $60,000.00 $369.86
02-Apr-2019 01-Jul-2019 91 2.60% $60,369.86 $391.33
02-Jul-2019 01-Oct-2019 92 2.70% $60,761.19 $413.51
02-Oct-2019 01-Jan-2020 92 2.80% $61,174.70 $431.74
Maturity 365 $61,606.44
September 14, 2019
3:01 pm
hwyc
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@CHUCK21
AFTER EXCLUDING THE COMPUNDING OF INTEREST, YOU ALSO NEED TO ASSUME FOUR IDENTICAL INTERVALS - NOT 90, 91, 92, 92 DAYS. BECAUSE 2.65% IS THE AVERAGE, NOT THE WEIGHTED AVERAGE OF THE QUARTERLY RATES. THEN THE SUM OF YOUR FOUR QUARTERLY INTEREST WILL ADD UP TO $1590

HOPE THIS HELPS.

September 14, 2019
3:20 pm
Norman1
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THE EQUIVALENT ANNUALLY-COMPOUNDED ONE-YEAR GIC RATE IS THE SLIGHTLY HIGHER GEOMETRIC AVERAGE OF THE QUARTERLY RATES AND NOT THE SIMPLE ARITHMETIC AVERAGE OF 2.65%: The equivalent annually-compounded one-year GIC rate is the slightly higher geometric average of the quarterly rates and not the simple arithmetic average of 2.65%:
CAGR = (1 + 90/365 * 2.5%)(1 + 91/365 * 2.6%)(1 + 92/365 * 2.7%)(1 + 92/365 * 2.8%) - 1
= (1 + 0.0061644)(1 + 0.0064822)(1 + 0.0068055)(1 + 0.0070575) - 1
= 1.026774 - 1
= 0.026774
= 2.6774%
September 15, 2019
8:38 am
Winnie
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Norman1 said
I GET SLIGHTLY DIFFERENT AMOUNTS FOR THE LAST TWO QUARTERS. BUT, I THINK WE HAVE THE RIGHT IDEA:
  

You are correct, Norman1.

I just recopied CHUCK21 calculations.

I'm sorry, next time will do my own proper calculations.

I corrected my post #21 now.

Thanks, Norman1.

September 15, 2019
8:59 am
CHUCK21
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HI GOJETSGO,
THANKS FOR NOTICING THE ERROR. I HAVE RECALCULATED THE ENTIRE EXERCISE AND FIND THAT THE QUARTERLY INTEREST PAYMENTS STILL RETURN ABOUT $100.00 MORE THAN THE AVERAGE INTEREST RATE.

TO MY WAY OF THINKING, AND DISREGARDING THE OTHER QUARTERLY PERKS, A COMPETITORS INTEREST RATE ONLY HAS TO BE .05% HIGHER THAN HUBERT`S AVERAGE TO RECEIVE THE SAME RETURN.

September 15, 2019
11:48 am
Norman1
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I THINK THE ARITHMETIC IS STILL OFF. I think the arithmetic is still off.
WINNIE AND I CALCULATED THE DIFFERENCE TO BE AROUND $16.44. THAT WORKS OUT TO BE ONLY 2.6774% - 2.65% = 0.0274% ABOVE THE 2.65% AVERAGE. Winnie and I calculated the difference to be around $16.44. That works out to be only 2.6774% - 2.65% = 0.0274% above the 2.65% average.
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