amort.period: Amortization Period

In FinancialMath: Financial Mathematics for Actuaries

Description

Solves for either the number of payments, the payment amount, or the amount of a loan. The payment amount, interest paid, principal paid, and balance of the loan are given for a specified period.

Usage

amort.period(Loan=NA,n=NA,pmt=NA,i,ic=1,pf=1,t=1)

Arguments

Loan	loan amount
n	the number of payments/periods
pmt	value of level payments
i	nominal interest rate convertible ic times per year
ic	interest conversion frequency per year
pf	the payment frequency- number of payments per year
t	the specified period for which the payment amount, interest paid, principal paid, and loan balance are solved for

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

Loan=pmt*{a_{≤ft. {\overline {\, n \,}}\! \right |j}}

Balance at the end of period t: B_t=pmt*{a_{≤ft. {\overline {\, n-t \,}}\! \right |j}}

Interest paid at the end of period t: i_t=B_{t-1}*j

Principal paid at the end of period t: p_t=pmt-i_t

Value

Returns a matrix of input variables, calculated unknown variables, and amortization figures for the given period.

Note

Assumes that payments are made at the end of each period.

One of n, pmt, or Loan must be NA (unknown).

If pmt is less than the amount of interest accumulated in the first period, then the function will stop because the loan will never be paid off due to the payments being too small.

If the pmt is greater than the loan amount plus interest accumulated in the first period, then the function will stop because one payment will pay off the loan.

t cannot be greater than n.

Author(s)

Kameron Penn and Jack Schmidt

See Also

amort.table

Examples

amort.period(Loan=100,n=5,i=.01,t=3)

amort.period(n=5,pmt=30,i=.01,t=3,pf=12)

amort.period(Loan=100,pmt=24,ic=1,i=.01,t=3)

Example output

           Amortization
Loan          100.00000
PMT            20.60398
Eff Rate        0.01000
Years           5.00000
At Time 3:      3.00000
Int Paid        0.60596
Princ Paid     19.99802
Balance        40.59798
           Amortization
Loan         149.627429
PMT           30.000000
Eff Rate       0.010000
i^(12)         0.009954
Periods        5.000000
Years          0.416667
At Time 3:     3.000000
Int Paid       0.074535
Princ Paid    29.925465
Balance       59.925424
           Amortization
Loan         100.000000
PMT           24.000000
Eff Rate       0.010000
Years          4.277206
At Time 3:     3.000000
Int Paid       0.537700
Princ Paid    23.462300
Balance       30.307700

FinancialMath documentation built on May 1, 2019, 11:16 p.m.