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Chapter 5: Q. 21 (page 324)

Find the principal needed now to get each amount; that is, find the present value to get $80 after 314 years at 9% compounded continuously

Short Answer

Expert verified

The answer is $59.71

Step by step solution

01

Step 1. Given information 

The amount, A=$80

The rate of interest, r=9%=9100=0.09

The time period, t=314=134years

The investment compounded continuously.

02

Step 2. Use Present value formulas

The present value P of A dollars received after t years, assuming a per annum interest rate r compounded continuously isP=Ae-rt

03

Step 3. Calculation

Substitute the values in the Present value formula,

P=$80e-0.09脳134P=$80e-0.2925P=$800.367870.2925P=$800.74639P=$59.71

The Present value,P=$59.71

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