So why doesn't the following equation yield zero: Time Payment Rate Balance $579.75 0 $100 1% ($579.75-100)*1.01=484.54 1 $100 1% ($484.54-100)*1.01=388.39 2 $100 1% ($388.39-100)*1.01=291.27 3 $100 2% ($291.27-100)*1.02=195.10 4 $100 2% ($195.10-100)*1.02=97.00 5 $100 2% ($97-100)*1.02=-3.06 The final figure should be zero if the PV is correct, but its not so either my logic is wrong or my math is wrong. Please help.
I calculated the PV value of a $100 payment stream at 1% for 6 years payable at the beginning of the year to be $585.34.
Likewise, if I have a balance today of $584.34 in 6 years this balance would be paid off if I deduct $100 at the beginning of each year at 1% interest.
(See image capture 1)
However I run into issues whe I use two interest rates.
Time Payment Rate PV
0 $100 1% 100/(1.01)^0=100
1 $100 1% 100/(1.01)^1=99.01
2 $100 1% 100/(1.01)^2=98.03
3 $100 2% 100/((1.01)^2*(1.02))=96.11
4 $100 2% 100/((1.01)^2*(1.02)^2)=94.22
5 $100 2% 100/((1.01)^2*(1.02)^3)=92.38
The Total PV for this stream is $579.75.
So why doesn't the following equation yield zero:
Time Payment Rate Balance
$579.75
0 $100 1% ($579.75-100)*1.01=484.54
1 $100 1% ($484.54-100)*1.01=388.39
2 $100 1% ($388.39-100)*1.01=291.27
3 $100 2% ($291.27-100)*1.02=195.10
4 $100 2% ($195.10-100)*1.02=97.00
5 $100 2% ($97-100)*1.02=-3.06
The final figure should be zero if the PV is correct, but its not so either my logic is wrong or my math is wrong. Please help.
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