# Solve Compound Interest Problems using the Ti 84 Calculator

To solve compound interest problems, it’s important to know exactly what they are. Compound interest problems consider the investment of a sum of money, to which periodic interest credits are made. The next period’s credit is made upon the total.

A = Compounded Amount (2000)

P = Original Principal (1000)

R = Annual interest Rate (.0695152928)

N = Number of compounding per year (12)

T = Number of years (10)

Problems may require that this formula be solved for any one of the above. To follow the examples, begin by storing the specified values into the variables.

This can be accomplished, by algebraic methods, for any variable other than N. Algebraic solutions for R and T, using (base 10) logarithms:

R=N (10^ (Log (A/P)/ (NT))-1) Annual Rate, when compounded N times per year for T years

T=Log (A/P)/ (NLog ((R+N)/N) Number of years, when compounded N times per year

These expressions can be evaluated using pencil and paper, or a four-function calculator, and a table of logarithms. In an Algebra II class, where logarithms are part of the subject matter, the teacher may prohibit the use of calculators, and/or require that work, involving use of logarithms, be shown.

The TI-84 has the capability to solve compound interest problems including the above formula. A=P (1+R/N) ^ (NT)—for any single variable, using a numerical-approximation approach. To see this (go thru the Catalog to access the Solve (function) :

Solve (A-P (1+R/N) ^ (NT),?, 0) ? may be any variable, including N

Try this, for all five variables each of the above values should be returned. Then, if desired, change one or more values, retry the operation, and observe the change in results. (If R is reduced below around .069315, no value of N will work; a “no sign chng” error will be returned).

When trying to solve compound interest problems, use of the Solve (function) is somewhat more straightforward, but it is also advisable to become familiar with the use of logarithms. The basic formula is: A=P (1+R/N) ^ (NT). Assume that the values, for use in examples, are:

A = Compounded Amount (2000)

P = Original Principal (1000)

R = Annual interest Rate (.0695152928)

N = Number of compounding per year (12)

T = Number of years (10)

Problems may require that this formula be solved for any one of the above. To follow the examples, begin by storing the specified values into the variables.

This can be accomplished, by algebraic methods, for any variable other than N. Algebraic solutions for R and T, using (base 10) logarithms:

R=N (10^ (Log (A/P)/ (NT))-1) Annual Rate, when compounded N times per year for T years

T=Log (A/P)/ (NLog ((R+N)/N) Number of years, when compounded N times per year

These expressions can be evaluated using pencil and paper, or a four-function calculator, and a table of logarithms. In an Algebra II class, where logarithms are part of the subject matter, the teacher may prohibit the use of calculators, and/or require that work, involving use of logarithms, be shown.

The TI-84 has the capability to solve compound interest problems including the above formula. A=P (1+R/N) ^ (NT)—for any single variable, using a numerical-approximation approach. To see this (go thru the Catalog to access the Solve (function) :

Solve (A-P (1+R/N) ^ (NT),?, 0) ? may be any variable, including N

Try this, for all five variables each of the above values should be returned. Then, if desired, change one or more values, retry the operation, and observe the change in results. (If R is reduced below around .069315, no value of N will work; a “no sign chng” error will be returned).

When trying to solve compound interest problems, use of the Solve (function) is somewhat more straightforward, but it is also advisable to become familiar with the use of logarithms. The basic formula is: A=P (1+R/N) ^ (NT). Assume that the values, for use in examples, are: