Problem 3(a) If Daniella opens a mutual fund account with a deposit of $15,000 and it promises topay an annual interest rate of r%, compounded on a monthly basis.(i) Derive a function B, which shows the balance on Daniella's account the end of 6 years.(11) Make a comparison of the rates of change in B with resect to the interest rate when r is8% , 10% and 12%.

Answered: (a) If Daniella opens a mutual fund…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter5: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 14P: Annual interest yield refer to problem 13 .suppose the investor decides to increase the maximum...

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Problem 3
(a) If Daniella opens a mutual fund account with a deposit of $15,000 and it promises to
pay an annual interest rate of r%, compounded on a monthly basis.
(i) Derive a function B, which shows the balance on Daniella's account the end of 6 years.
(11) Make a comparison of the rates of change in B with resect to the interest rate when r is
8% , 10% and 12%.

Expert Solution

Step 1

Given that the deposit amount = $ 15,000, annual interest rate = r % and it is compounded on monthly basis.

(i):

Now, we have to find function B for balance at end of 6 years:

A = final amount

P = principal amount,

r = interest rate,

n = number of times interest applied per time period, and

t = number of time periods elapsed

$A = P {(1 + \frac{r}{n})}^{n t} Let B (r) is the balance on daniella's account the end of 6 years: B (r) = (15000) {(1 + \frac{r}{100 \times 12})}^{12 \times 6} = (15000) {(1 + \frac{r}{1200})}^{72}$

Step 2

Now, the rate of change of B with respect to interest rate is dB(r)/dr :

$B (r) = (15000) {(1 + \frac{r}{1200})}^{72} \frac{d}{d r} B (r) = (15000) \{(72) {(1 + \frac{r}{1200})}^{72 - 1}\} \frac{1}{1200} = \frac{15000}{1200} [72 {(1 + \frac{r}{1200})}^{71}] = 900 {(1 + \frac{r}{1200})}^{71}$

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