In the case of a interest-earning savings account, one would follow the equation
Present Value =
(Principal+Interest) Times
(1 + {Percent Rate/Yearly Compounding Frequency})-(Years Invested×Yearly Compounding Frequency).
Take an example with:
PV equal to $23121;
Percent Rate = 10.8%;
Yearly Compounding Frequency = Every Two Months Or Six Times Per Year;
Years Invested = 10.
Placement of these values in the equation gives
$23121 = (Principal + Interest) × (1 + {0.108/6})-(10×6)
which will isolate (Principal + Interest) as $67433.12616
or $67433.13.
Then $23121.00 is the Present Value that must be invested at
10.8% compounded every two months to gain $67433.13 in 10
years.
Interest earned on the initial $23121.00 over 10 years would be
$67433.13 − $23121.00 or $44312.13.
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In the case of an ordinary, interest-earning annuity, one would follow the equation
Present Value =
(Contribution To Annuity Every Payment Period) Times
{1 − [1 + (Percent Rate / Compounding Frequency)]-(Years Invested × Yearly Compounding Frequency)}
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(Percent Rate / Compounding Frequency)
Use the specific data below to build the example for an annuity:
PV equal to $23121;
Percent Rate = 10.8%;
Yearly Compounding Frequency = Every Two Months Or Six Times Per Year;
Years Invested = 10;
Then write $23121.00 = (Contribution To Annuity Every Payment Period) ×
{1 − [1 + (0.108/6)]-(10×6)} ÷ (0.108/6).
This isolates the payment to the annuity every two months as
$23121.00 divided by [{1 − [1 + (0.108/6)]-(10×6)} ÷ (0.108/6)] or
$23121.00 divided by 36.50705413 or 633.3296551 or $633.33.
