Question

Please assist me with the following compound interest problems.​

Answer 1

Answer:

  see the attachments below

Step-by-step explanation:

When the calculations are repetitive using the same formula, it is convenient to put the formula into a spreadsheet and let it do the calculations.

That is what was done for the spreadsheet below. The formula used is the one given in the problem statement.

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For doubling time, the formula used is the one shown in the formula bar in the attachment. (For problem 11, the quarterly value was used instead of the monthly value.) It makes use of the growth factor for the period used for the rest of the problem.

The doubling time is in years.

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The doubling time can also be found using a graphing calculator. In the second attachment, we have written a function that shows the multiplier for a given interest rate r and compounding n. The x-intercept in each case is the solution for t that makes the multiplier be 2. The steeper curve is associated with the higher interest rate.

Answer 2

Answer:  See Below

Step-by-step explanation:

NOTES: Annually → n = 1

             Bi-Annually → n = 2

             Quarterly → n = 4

             Monthly → n = 12

             Daily → n = 365

             $A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}$        

            "A" must be rounded to the hundredth place

11) Given: P = 2000, r = 8% (.08), t = 5

$\text{Annually:}\quad A=2000\bigg(1+\dfrac{.08}{1}\bigg)^{1(5)}\quad =\quad \ 2938.66\\\\\\\text{Bi-Annually:}\quad A=2000\bigg(1+\dfrac{.08}{2}\bigg)^{2(5)}\quad =\quad \ 2960.49\\\\\\\text{Quarterly:}\quad A=2000\bigg(1+\dfrac{.08}{4}\bigg)^{4(5)}\quad =\quad \ 2971.89\\\\\\\text{Monthly:}\quad A=2000\bigg(1+\dfrac{.08}{12}\bigg)^{12(5)}\quad =\quad \ 2979.69\\\\\\\text{Daily:}\quad A=2000\bigg(1+\dfrac{.08}{365}\bigg)^{365(5)}\quad =\ 2983.52$

12) Given: P = 500, r = 2% (.02), t = 3

$\text{Annually:}\quad A=500\bigg(1+\dfrac{.02}{1}\bigg)^{1(3)}\quad =\quad \ 530.60\\\\\\\text{Bi-Annually:}\quad A=500\bigg(1+\dfrac{.02}{2}\bigg)^{2(3)}\quad =\quad \ 530.76\\\\\\\text{Quarterly:}\quad A=500\bigg(1+\dfrac{.02}{4}\bigg)^{4(3)}\quad =\quad \ 530.84\\\\\\\text{Monthly:}\quad A=500\bigg(1+\dfrac{.02}{12}\bigg)^{12(3)}\quad =\quad \ 530.89\\\\\\\text{Daily:}\quad A=500\bigg(1+\dfrac{.02}{365}\bigg)^{365(3)}\quad =\ 530.92$