Sinking fund amortization schedule for a loan

Builds a sinking fund schedule under a fixed loan rate and a fixed accumulation rate for the sinking fund, using compact actuarial notation.

Usage

sinking_fund_schedule(
  principal,
  n,
  i,
  j,
  k = 1L,
  i_type = "effective",
  j_type = "effective",
  m = 1L,
  j_m = 1L,
  deposit = NULL,
  tol = 1e-08
)

Arguments

principal: Numeric scalar. Initial loan amount.
n: Positive integer. Number of schedule periods.
i: Numeric scalar. Annual interest-rate input for the loan.
j: Numeric scalar. Annual accumulation-rate input for the sinking fund.
k: Positive integer. Number of schedule periods per year.
i_type: Character string indicating the loan interest-rate type. Allowed values are "effective", "nominal_interest", "nominal_discount", and "force".
j_type: Character string indicating the sinking-fund accumulation-rate type. Allowed values are "effective", "nominal_interest", "nominal_discount", and "force".
m: Positive integer. Conversion frequency for nominal loan rates. Validated for every rate family, although it affects conversion only for nominal rates.
j_m: Positive integer. Conversion frequency for nominal sinking-fund rates. Validated for every rate family, although it affects conversion only for nominal rates.
deposit: Optional numeric scalar. Level sinking-fund deposit per period. If NULL, it is computed so that the fund accumulates to principal at the end of period n (n / k years).
tol: Finite positive numeric tolerance in monetary units used for final-balance checks.

Value

A tibble with one row per period and columns:

period: Period index.
loan_balance_start: Outstanding loan balance at the start of the period.
interest_loan: Interest paid on the loan during the period.
sinking_deposit: Deposit made into the sinking fund.
fund_balance_start: Fund balance at the start of the period.
interest_fund: Interest earned by the fund during the period.
fund_balance_end_before_redemption: Fund balance before final redemption.
redemption_from_fund: Amount withdrawn from the fund to redeem the loan at maturity.
fund_balance_end: Fund balance after redemption.
loan_balance_end: Outstanding loan balance after redemption.
total_cashflow_borrower: Borrower's external cash outflow during the period.
i_effective_loan_annual: Equivalent annual effective loan rate.
i_effective_fund_annual: Equivalent annual effective fund rate.
i_loan_period: Effective loan rate per schedule period.
i_fund_period: Effective fund rate per schedule period.
k: Schedule frequency.

Details

The borrower pays:

interest on the loan each period, and
a level deposit into the sinking fund.

At maturity, the sinking fund is used to redeem the principal.

This function follows the compact actuarial notation used throughout tidyactuarial: i is the loan interest rate, j is the sinking-fund accumulation rate, k is the number of schedule periods per year, m is the conversion frequency for the loan rate, and j_m is the conversion frequency for the sinking-fund rate.

The supplied annual rate specifications are converted to effective annual rates and then to effective rates per schedule period: $$i_p = (1+i_e)^{1/k} - 1,\qquad j_p = (1+j_e)^{1/k} - 1.$$

If deposit is NULL, the unit-payment accumulation sum is evaluated stably from the original log fund rate. Only an exactly zero rate uses the zero-rate limit principal / n. The monetary balance tolerance does not determine whether a rate is zero. The existing requirement of finite annual and period equivalents is retained. Non-finite monetary ledger entries cause an explicit error. A user-supplied deposit is not adjusted to force exact redemption: any uncovered loan balance or fund surplus remains in the corresponding final column and triggers the existing mismatch warning when it exceeds tol. Redemption from the fund is an internal transfer and is not counted again in the borrower's external cash flow. Storage grows with n; feasible terms are limited by integer indexing and available memory.

Otherwise, the standard sinking-fund formula is used: $$deposit = \frac{principal}{s_{\overline{n}|j_p}}$$ where $$s_{\overline{n}|j_p} = \frac{(1+j_p)^n - 1}{j_p}.$$

Examples

sinking_fund_schedule(
  principal = 100000,
  n = 12,
  i = 0.12,
  j = 0.096,
  i_type = "nominal_interest",
  j_type = "nominal_interest",
  m = 12,
  j_m = 12,
  k = 12
)
#> # A tibble: 12 × 16
#>    period loan_balance_start interest_loan sinking_deposit fund_balance_start
#>     <int>              <dbl>         <dbl>           <dbl>              <dbl>
#>  1      1             100000          1000           7973.                 0 
#>  2      2             100000          1000           7973.              7973.
#>  3      3             100000          1000           7973.             16010.
#>  4      4             100000          1000           7973.             24111.
#>  5      5             100000          1000           7973.             32277.
#>  6      6             100000          1000           7973.             40508.
#>  7      7             100000          1000           7973.             48805.
#>  8      8             100000          1000           7973.             57168.
#>  9      9             100000          1000           7973.             65599.
#> 10     10             100000          1000           7973.             74097.
#> 11     11             100000          1000           7973.             82662.
#> 12     12             100000          1000           7973.             91297.
#> # ℹ 11 more variables: interest_fund <dbl>,
#> #   fund_balance_end_before_redemption <dbl>, redemption_from_fund <dbl>,
#> #   fund_balance_end <dbl>, loan_balance_end <dbl>,
#> #   total_cashflow_borrower <dbl>, i_effective_loan_annual <dbl>,
#> #   i_effective_fund_annual <dbl>, i_loan_period <dbl>, i_fund_period <dbl>,
#> #   k <int>

sinking_fund_schedule(
  principal = 50000,
  n = 10,
  i = 0.02,
  j = 0,
  deposit = NULL
)
#> # A tibble: 10 × 16
#>    period loan_balance_start interest_loan sinking_deposit fund_balance_start
#>     <int>              <dbl>         <dbl>           <dbl>              <dbl>
#>  1      1              50000          1000            5000                  0
#>  2      2              50000          1000            5000               5000
#>  3      3              50000          1000            5000              10000
#>  4      4              50000          1000            5000              15000
#>  5      5              50000          1000            5000              20000
#>  6      6              50000          1000            5000              25000
#>  7      7              50000          1000            5000              30000
#>  8      8              50000          1000            5000              35000
#>  9      9              50000          1000            5000              40000
#> 10     10              50000          1000            5000              45000
#> # ℹ 11 more variables: interest_fund <dbl>,
#> #   fund_balance_end_before_redemption <dbl>, redemption_from_fund <dbl>,
#> #   fund_balance_end <dbl>, loan_balance_end <dbl>,
#> #   total_cashflow_borrower <dbl>, i_effective_loan_annual <dbl>,
#> #   i_effective_fund_annual <dbl>, i_loan_period <dbl>, i_fund_period <dbl>,
#> #   k <int>

Usage

Arguments

Value

Details

See also

Examples