Tag Archives: PAYMENT

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()

PV()

Posted on by vivaclipper

PV()

Present value of a loan

Syntax

      PV( nPayment, nInterest, nPeriods ) --> nPresentValue

Arguments

<nPayment> amount of money paid back per period <nInterest> rate of interest per period, 1 == 100%

<nPeriods> period count

Returns

<nPresentValue> Present value of a loan when one is paying back <nDeposit> per period at a rate of interest of <nInterest> per period

Description

PV() calculates the present value of a loan that is paid back in <nPeriods> payments of <nPayment> (Dollars, Euros, Yens, …)
while the rate of interest is <nInterest> per period:
debt in period 0 = <nPresentValue>
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

    <nPresentValue> = <nPayment>*(1-(1+<nInterest>/100)ˆ(-n)) / (<nInterest>/100)

Examples

      // You can afford to pay back 100 Dollars per month for 5 years
      // at a interest rate of 0.5% per month (6% per year), so instead
      // of 6000 Dollars (the amount you will pay back) the bank will pay
      // you

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

Tests

      pv( 100, 0.0, 60 )   == 6000.0
      pv( 100, 0.005, 60 ) == 5172.56

Compliance

PV() is compatible with CT3’s PV().

Platforms

All

Files

Source is finan.c, library is libct.

Seealso

FV(), PAYMENT(), PERIODS(), 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_PAYMENT

Posted on by vivaclipper 
 PAYMENT()
 Computes the periodic payment amount
------------------------------------------------------------------------------
 Syntax

     PAYMENT(<nCapital>,<nInterestRate>,<nNumberpayments>,)
         --> nPayment

 Arguments

     <nCapital>  Designates the loan amount.

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

     <nNumberPayments>  Designates the number of payments on the loan
     within the payment period.

 Returns

     PAYMENT() returns the payment to make for each payment period.

 Description

     PAYMENT() computes the payment for each period where loan interest
     applies.  The determined amount relates to a loan amount <nCapital> that
     is repaid over <nNumberPayments>, at an interest rate of
     <nInterestRate>.

 Example

     How high does the monthly annuity amount have to be, if you want to
     repay a $2,000.00 loan within 24 months at an annual interest rate of
     10%:

     nRate  :=  0.1/12              // The monthly rate
     ? PAYMENT(2000, Rate, 24)      // 92.29 per month

See Also: PV() FV() RATE() PERIODS()




			

	
	



		
			


	

		
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