To solve a continuous compounding problem complete these steps:

1.Compute the annual effective rate using the above equation.

2.Either use this effective rate in your calculations with an annual period (P/YR = 1) or convert this rate so that it applies to your payment period. In the following example, P/YR = 12 so you have to calculate a new NOM% using the interest rate conversion application with P/YR equal to 12.

Example

You currently have 4,572.80 in an account at Dream World Investments that earns 18% annual interest compounded continuously. At the end of each month, you deposit 250.00 in the account. What will the balance be after 15 years?

Table 13-6 Calculating the annual nominal rate

KeysDisplay Description

Jg§

0.18

Divides nominal rate by 100.

 

 

 

 

\K

1.20

Raises e to 0.18 power.

 

 

 

 

AJPJ::4

19.72

Calculates annual effective rate.

 

 

 

 

\Ð

19.72

Stores effective rate.

 

 

 

 

JG\Í

12.00

Sets payments per year.

 

 

 

 

\Ó

18.14

Calculates the annual nominal

 

rate for a monthly payment

period.

Set to End Mode. Press \¯if BEGIN annunciator is displayed.

Table 13-7 Calculating the balance amount after 15 years

KeysDisplay Description

JV\Ú

180.00

Stores number of months.

 

 

 

 

GV:yÌ

-250.00

Stores regular payment.

 

 

 

 

YVjG7gy

 

negative value (like an initial

 

-4,572.80

Stores current balance as a

Ï

 

investment).

 

 

 

 

 

É

297,640.27

Calculates the account balance

 

after 15 years of payments with

18% interest compounded continuously.

140 Additional Examples