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Chapter 5: Q. 22 (page 324)

Find the principal needed now to get each amount; that is, find the present value to get $800 after 212 years at 8% compounded continuously.

Short Answer

Expert verified

The answer is $654.98

Step by step solution

01

Step 1. Given information 

The amount, A=$800

The rate of interest, r=8%=8100=0.08

The time period,t=212=52years

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, is P=Ae-rt

03

Step 3. Calculation

Substitute the values in the Present value formula,

P=$800e-0.08脳52P=$800e-0.2P=$8001e0.2P=$8000.367870.2P=$8000.81873P=$654.98

The Present value,P=$654.98

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