4. Suppose a fund accumulates according to the force of interest 8 (t) = { a 0.05 ct (10-t) 0St≤ 10 t> 10 where c> 0. A deposit in the amount of 5000 is made at the end of two years, and a deposit of 10,000 is made at the end of 10 years. At the end of 20 years, a withdrawal of 100,000 is made to empty out the fund, and then the account is closed.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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4. Suppose a fund accumulates according to the force of interest
={
ct (10-t) 0≤t≤ 10
0.05
t > 10
8 (t)=
where c > 0.
A deposit in the amount of 5000 is made at the end of two years, and a
deposit of 10,000 is made at the end of 10 years. At the end of 20 years, a
withdrawal of 100,000 is made to empty out the fund, and then the account is
closed.
(a) Find c.
(b) Find the equivalent annual effective interest rate over the period (2, 10).
That is to say if the annual effective interest rate were constant over this time
period, what would it have to be?
Transcribed Image Text:4. Suppose a fund accumulates according to the force of interest ={ ct (10-t) 0≤t≤ 10 0.05 t > 10 8 (t)= where c > 0. A deposit in the amount of 5000 is made at the end of two years, and a deposit of 10,000 is made at the end of 10 years. At the end of 20 years, a withdrawal of 100,000 is made to empty out the fund, and then the account is closed. (a) Find c. (b) Find the equivalent annual effective interest rate over the period (2, 10). That is to say if the annual effective interest rate were constant over this time period, what would it have to be?
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