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Sharp EL-512 program for mortgage payment calculation - striegel - 09-05-2015 09:26 PM
In the little pocket of the plastic case for my 1981 Sharp EL-512 scientific calculator I keep two hand-written slips of paper to remind me of the formula I have programmed into its program memory. Sharp refers to the program memory as the "Multi Formula Reserve" since there are four keys that can store one formula each.
The papers are not dated, but I'm certain they were written back around the time I was buying my first house in 1987. The formula is not expressed in banker terms, but serves the purpose of calculating the monthly payment on a conventional mortgage here in the US.
The following notes explain everything needed.
To figure monthly payment when using annual interest rate (compounded monthly)
$$Payment\quad =\frac { (Amount\quad of\quad loan)\quad \times \quad \cfrac { 1 }{ 12 } (Rate) }{ 1-\cfrac { 1 }{ { (1\quad +\quad \cfrac { 1 }{ 12 } (Rate)) }^{ 12\times (Years) } } } \\$$\( { K }_{ 7 }\quad =\quad Amount\\
{ \\ K }_{ 8 }\quad =\quad \frac { Rate }{ 12 }
\\ { K }_{ 9 }\quad =\quad Months\\
\)$$ \frac { { K }_{ 7 }\quad \times \quad { K }_{ 8 } }{ 1-\cfrac { 1 }{ { \left( 1\quad +\quad { K }_{ 8 } \right) }^{ { K }_{ 9 } } } } \\ $$
\( { K }_{ n }8\quad +\quad 1\quad =\quad { y }^{ x }\quad { K }_{ n }9\quad =\quad 1/x\quad +/-\quad +\quad 1\quad =\quad 1/x\quad \times \quad { K }_{ n }7\quad \times \quad { K }_{ n }8\quad =\)
\( \boxed { LRN } \quad \boxed { 1: } \\ \boxed { STO } \quad \boxed { 7 } \quad \\ \boxed { \left( x \right) } \quad \boxed { \times } \quad \boxed { 1 } \quad \boxed { 2 } \quad \boxed { = } \quad \boxed { STO } \quad \boxed { 9 } \\ \boxed { \left( x \right) } \quad \boxed { \times } \quad \boxed { . } \quad \boxed { 0 } \quad \boxed { 1 } \quad \boxed { \div } \quad \boxed { 1 } \quad \boxed { 2 } \quad \boxed { = } \quad \boxed { STO } \quad \boxed { 8 } \\ \boxed { + } \quad \boxed { 1 } \quad \boxed { = } \quad \boxed { { y }^{ x } } \quad \boxed { Kn } \quad \boxed { 9 } \quad \boxed { = } \quad \\ \boxed { 1/x } \quad \boxed { +/- } \quad \boxed { + } \quad \boxed { 1 } \quad \boxed { = } \\ \boxed { 1/x } \quad \boxed { \times } \quad \boxed { { Kn } } \quad \boxed { 7 } \quad \boxed { \times } \quad \boxed { Kn } \quad \boxed { 8 } \quad \boxed { = } \\ \boxed { LRN } \)
To use the above program:
Enter Amount Press \(\boxed { 1: } \)
Enter Years Press \(\boxed {COMP}\)
Enter Rate Press \(\boxed {COMP}\)