Advance payment and subsequent payment

Payments can only be compared if they occur at the same time. Because a payment that comes on January 1st of a year ( advance payment ) is worth more than one that comes at the end of the year ( subsequent payment ). In this case, the difference in value is exactly one annual discount rate , as the money that is received on January 1st can be invested at the discount rate for another year up to the point of comparison in t = 1 . The relationships between advance and subsequent installments are represented by the four basic formulas of the pension calculation .

Examples

Advance payment

• Rent usually has to be paid on the 1st of each month
• Old-age pensions are paid on the 1st of the month
• Maintenance contracts are often due at the beginning of the year
• Insurance contributions are usually payable at the beginning of the year
• Leasing installments are due at the beginning of the month
• Advance perpetual (annual) annuity:

${\displaystyle {\ddot {a}}_{\overline {\infty |}}=1+v+v^{2}+v^{3}+\cdots ={\frac {1}{1-v}}}$

Excess

• Salaries are usually only paid at the end of the month
• Loan installments are only due at the end of the month
• New pensions are transferred at the end of the month
• Additional perpetual (annual) annuity:

${\displaystyle \,a_{\overline {\infty |}}=v+v^{2}+v^{3}+\cdots ={\frac {v}{1-v}}}$

See also

• Pension bill