Casio FXCP400 NPV, IRR, NPV, IRR, NPV, PBP, n –, CFk, NPV, NPV, NPVn, NPVn = Σ, (1 + i)k, (CF0 t 0), Amortization, NPVn+1 – NPVn, Interest Conversion

In this formula, NPV = 0, and the value of IRR is equivalent to i × 100. It should be noted, however, that minute fractional values tend to accumulate during the subsequent calculations performed automatically by the ClassPad, so NPV never actually reaches exactly zero. IRR becomes more accurate the closer that NPV approaches to zero.

	{	0 ..................................					(CF0 t 0)
PBP =		n –			NPVn		... (Other than those above)
				NPVn+1 – NPVn
		n		CFk		n: smallest positive integer that satisfies the conditions
NPVn = Σ
			(1 + i)k			NPVn s 0, 0 s NPVn+1, or 0
	k = 0

Amortization

a e

1 payment

1 payment

c

d

b

1.............

PM1................

PM2.............

Last

1

............

PM1...................

PM2..........

Last

Number of payments

Number of payments

a: interest portion of payment PM1 (INT)

=1@PM1=I DG5PM1–1⋅I ⋅ (H2@)

b: principal portion of payment PM1 (PRN)

HJ1PM1=H2@+DG5PM1–1⋅

c: principal balance upon completion of

DG5PM2=DG5PM2–1 +HJ1PM2

payment PM2 (BAL)

d: total principal paid from payment PM1 to

Σ HJ1=HJ1PM1 +HJ1PM1+1 + … + HJ1PM2

PM2

payment PM2 (ΣPRN)

PM1

e: total interest paid from payment PM1 to

a + b = one repayment (PMT)

payment PM2 (ΣINT)

ΣPM2

PM1

=1@==1@PM1 +=1@PM1+1 + … + =1@PM2

BAL0 = PV (when “Payment Date” is “End”)

INT1 = 0, PRN1 = PMT (when “Payment Date” is “Begin”)

Converting between the Nominal Interest Rate and Effective Interest Rate

The nominal interest rate (I% value input by user) is converted to an effective interest rate (I%') for installment loans where the number of annual payments is different from the number of annual compound calculation periods.

			[C/Y ]
I%' = {(1 +	I%			– 1}⋅ 100
			[P/Y ]
		)
	100 ⋅ [C/Y ]

The following calculation is performed after conversion from the nominal interest rate to the effective interest rate, and the result is used for all subsequent calculations.

i = I%' ⎟ 100

Interest Conversion

		APR/100	n					1
EFF =	1 +			⋅ 100	APR =	1 +	EFF	n		⋅ n ⋅ 100
		n	– 1				100	– 1
									Chapter 11: Financial Application		184