Tag Archives: PV

PAYMENT()

Posted on by vivaclipper

PAYMENT()

Payments for a loan

Syntax

       PAYMENT( nLoan, nInterest, nPeriods ) --> nPayment

Arguments

<nLoan> amount of money you get from the bank

<nInterest> rate of interest per period, 1 == 100%

<nPeriods> period count

Returns

<nPayment> Periodical payment one has to make to pay the loan <nLoan> back

Description

PAYMENT() calculates the payment one has to make periodically to pay back a loan <nLoan> within <nPeriods> periods and for a rate of interest <nInterest> per period.

debt in period 0 = <nLoan>
debt in period 1 = ((debt in period 0)-<nPayment>)*(1+<nInterest>/100)
debt in period 2 = ((debt in period 1)-<nPayment>)*(1+<nInterest>/100)

etc…

debt in period <nPeriod> = ((debt in period <nPeriod>-1)-<nPayment>)*(1+<nInterest>/100)

 -> has to be 0, so <nPayment> = <nLoan>*(<nInterest>/100)/(1-(1+<nInterest>/100)ˆ(-n))

Examples

       // You get a loan of 5172.56 at a interest rate of 0.5% per
       // month (6% per year).
       // For 5 years, you have to pay back every month

       ? payment( 5172.56, 0.005, 60 ) // --> 100.00

Tests

       payment( 5172.56, 0.0, 60 )   == 86.21
       payment( 5172.56, 0.005, 60 ) == 100.00

Compliance

PAYMENT() is compatible with CT3’s PAYMENT().

Platforms

All

Files

Source is finan.c, library is libct.

Seealso

PV(), FV(), PERIODS(), RATE()

RATE()

Posted on by vivaclipper

RATE()

Estimate rate of interest for a loan

Syntax

      RATE( nLoan, nPayment, nPeriods ) --> nRate

Arguments

<nLoan> amount of money you get from the bank <nPayment> amount of money you pay back per period <nPeriods> number of periods you pay the loan back

Returns

<nInterest> estimated rate of interest per period, 1 == 100%

Description

RATE() calculates the rate of interest per period for the given loan, payment per periods and number of periods. This is done with the same equation used in the PAYMENT() or PERIODS() function:

<nPayment> = <nLoan>*(<nInterest>/100)/(1-(1+<nInterest>/100)ˆ(-<nPeriods>))

However, this equation can not be solved for <nInterest> in a “closed” manner, i.e. <nInterest> = …, so that the result can only be estimated.

Examples

      // You get a loan of 5172.56, pay 100 back every month for
      // 5 years (60 months). The effective interest rate per
      // period (=month) is

      ? rate( 5172.56, 100, 60 ) // --> 0.005

Tests

      rate( 5172.56, 100, 60.0 ) == 0.005
      rate( 6000.0, 100, 60.0 ) == 0.0

Compliance

RATE() is compatible with CT3’s RATE().

Platforms

All

Files

Source is finan.c, library is libct.

Seealso

PV(), FV(), PAYMENT(), PERIODS()

Periods()

Posted on by vivaclipper

Periods()

Number of Periods for a loan

Syntax

      Periods( nLoan, nPayment, nInterest ) --> nPeriods

Arguments

<nLoan> amount of money you get from the bank <nPayment> amount of money you pay back per period <nInterest> rate of interest per period, 1 == 100%

Returns

<nPeriods> number of Periods you need to pay the loan back

Description

Periods() calculates the number of Periods one needs to pay back a loan of <nLoan> with periodical payments of <nPayment> and for a rate of interest <nInterest> per period.

debt in period 0 = <nLoan>
debt in period 1 = ((debt in period 0)-<nPayment>)*(1+<nInterest>/100)
debt in period 2 = ((debt in period 1)-<nPayment>)*(1+<nInterest>/100) etc…
debt in period <nPeriod> = ((debt in period <nPeriod>-1)-<nPayment>)*(1+<nInterest>/100)

-> has to be 0, so

<nPeriods> = -log(1-<nLoan>*(<nInterest>/100)/<nPayment>)/log(1+<nInterest>/100))

Note, however that in the case of nPayment <= <nLoan>*(<nInterest>/100), one would need infinite time to pay the loan back. The functions does then return -1.

Examples

      // You get a loan of 5172.56 at a interest rate of 0.5% per
      // month (6% per year).
      // You can afford to pay 100 back every month, so you need

      ? Periods( 5172.56, 100, 0.005 ) // --> 60.0

      // months to cancel the loan.

Tests

      Periods( 5172.56, 100, 0.005 ) == 60.0
      Periods( 5172.56, 100, 0.0 ) == 51.7256

Compliance

Periods() is compatible with CT3’s Periods().

Platforms

All

Files

Source is finan.c, library is libct.

Seealso

PV(), FV(), PAYMENT(), RATE()

FV()

Posted on by vivaclipper

FV()

Future value of a capital

Syntax

      FV( nDeposit, nInterest, nPeriods ) --> <nFutureValue>

Arguments

<nDeposit> amount of money invested per period <nInterest> rate of interest per period, 1 == 100% <nPeriods> period count

Returns

<nFutureValue> Total value of the capital after <nPeriods> of paying <nDeposit> and <nInterest> interest being paid every period and added to the capital (resulting in compound interest)

Description

FV() calculates the value of a capital after <nPeriods> periods. Starting with a value of 0, every period, <nDeposit> (Dollars, Euros, Yens, …) and an interest of <nInterest> for the current capital are added for the capital (<nInterest>=Percent/100).

Thus, one gets the non-linear effects of compound interests:

value in period 0 = 0

value in period 1 = ((value in period 0)*(1+<nInterest>/100)) + <nDeposit>

value in period 2 = ((value in period 1)*(1+<nInterest>/100)) + <nDeposit> etc….

value in period <nPeriod> = ((value in period <nPeriod>-1)*(1+<nInterest>/100))< + <nDeposit>

                                           = <nDeposit> * sum from i=0 to <nPeriod>-1 over (1+<nInterest>/100)ˆi

                                          = <nDeposit> * ((1+<nInterest>/100)ˆn-1) / (<nInterest>/100)

Examples

      // Payment of 1000 per year for 10 years at a interest rate
      // of 5 per cent per year

      ? fv( 1000, 0.05, 10 ) // --> 12577.893

Tests

      fv( 1000, 0.00, 10 ) == 10000.0
      fv( 1000, 0.05, 10 ) == 12577.893

Compliance

FV() is compatible with CT3’s FV().

Platforms

All

Files

Source is finan.c, library is libct.

Seealso

PV(), PAYMENT(), PERIODS(), RATE()

CT_PV

Posted on by vivaclipper 
 PV()
 Computes the cash present value after interest charges
------------------------------------------------------------------------------
 Syntax

     PV(<nPayments>,<nInterestRate>,<nNumberPayments>)
        --> nCapital

 Arguments

     <nPayment>  Designates the amount of the scheduled periodic payment.

     <nInterestRate>  Designates the periodic interest rate.  1
     corresponds to 100%.

     <nNumberPayments>  Designates the number of anticipated payment
     periods.

 Returns

     PV() returns the cash value of an interest yield.

 Description

     PRESENT VALUE
     The function computes the cash value of regular equal payments
     <nNumberPayments> at an <nInterestRate> interest rate over
     <nNumberPayments> payment periods.

 Examples

     .  How high can a loan be if you pay $175 for 24 months, at an
        annual fixed interest rate of 9.5%?  Since payments are monthly, the
        annual percentage rate is divided by 12:

        nRate  :=  0.095/12
        ? PV(175, nRate, 24)     // $3811.43

     .  Annual payments over 2 years at 9.5% per annum:

        ? PV(175, 0.095, 2)      // $305.77

See Also: PAYMENT() RATE() PERIODS() FV()




			

	
	



		
			


	

		
Tools — Mathematical Functions


		

		Posted on  by vivaclipper		

	


		

		
Introduction Mathematical Functions
ACOS()    Computes the cosine arc
ASIN()    Computes the sine arc
ATAN()    Computes the tangent arc
ATN2()    Computes the angle size from the sine and cosine
CEILING() Rounds up to the next integer
COS()     Computes the cosine
COT()     Computes the cotangent
DTOR()    Converts from a degree to radian measure
FACT()    Computes the factorial
FLOOR()   Rounds down to the next integer
FV()      Computes future value of capital
GETPREC() Determines the level of precision that is set
LOG10()   Computes the common logarithm
PAYMENT() Computes the periodic payment amount
PERIODS() Computes number of payment periods necessary to repay a loan
PI()      Returns pi with the highest degree of accuracy
PV()      Computes the cash present value after interest charges
RATE()    Computes the interest rate for a loan
RTOD()    Converts from a radian to degree measure
SETPREC() Sets the precision level for trigonometric functions
SIGN()    Determines the mathematical sign of a number
SIN()     Computes the sine of a radian value
TAN()     Computes the tangent of a radian value