Can you help me solve this?

Question

On January 1, 2026 Janice put $450 in a savings account. She had to choose between two accounts. The account at her mothers bank pays 4.2% interest once at the end of the year. The account her fathers bank pays 3.8% interest twice every year. 

 

A. Assuming that Janice chose her Mother's bank, write the recursive formula that can be used to calculate the amount of money that Janice has in her account in terms of the number of times interest has been paid on the account.

 

B. If Janice chose yo use her Mother's bank, how much money will she have in January 2020? 

 

C. How long will it take for Janice to double her money?

 

D. How would your answers (for parts A, B, and C) change if Janice chose her Father's bank?

Answer 1

A.  Compound interest:  A = p(1+r/n)^nt

     A = future amount

     p = principal investment = $450

     r = interest rate as decimal = .042

     n = # times interest is compounded per year = 1

     t = time in years

 

     A = 450(1 + .042/1)^1(t)

     A = 450(1.042)^t

 

B.  Note:  You have the initial deposit made 1 January 2026

and want to know how much is in the account January 2020.

I will assume the 1 January 2026 is supposed to be 1 Jan 2016

giving a time frame of 4 years.

 

A = 450(1.042)⁴ = $________

 

plug into your calculator to find the total amount

 

C.  If Janice's money is doubled then the final amount

     A will be equal to twice the initial investment:

     A = 2(450) = 900

 

     900 = 450(1.042)^t

     2 = 1.042^t

     take log of both sides

     log 2 = log 1.042^t

     log 2 = t(log 1.042)

     log 2/log 1.042 = t

     t = 16.85 years

    

D.  If she used the other account the formula would

     change:  r = .038,  n = 2

 

    A = 450(1 + .038/2)^2t

    A = 450(1.019)^2t

 

   In January 2020:

   A = 450(1.019)²⁽⁴⁾

   A = 450(1.019)⁸

 

   Doubling her money:

   900 = 450(1.019)^t

   2 = 1.019^t

   log 2 = log 1.019^t

   log 2 = t(log 1.019)

   t = (log 2)/(log 1.019)