SOLUTION: Brooke invested $16,700 in a mutual fund at 2.8% compounded monthly. After 2 years, the interest rate was changed to 8.6% compounded quarterly. a) How much was the value of the

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Brooke invested $16,700 in a mutual fund at 2.8% compounded monthly. After 2 years, the interest rate was changed to 8.6% compounded quarterly. a) How much was the value of the       Log On

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Question 1192869: Brooke invested $16,700 in a mutual fund at 2.8% compounded monthly. After 2 years, the interest rate was changed to 8.6% compounded quarterly.
a) How much was the value of the fund 5 years after the rate change? $

b) How much was the total compound interest earned during the whole term?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
for the first 2 years, the number of time periods = 2 * 12 = 24 months and the interest rate per time period = 2.8% per year / 12 = .233333.....% per month.
the future value becomes 17,660.73.
that becomes the present value for the next 3 years.
the interest rate for the next 3 years becomes 8.6% per year / 4 = 2.15% per quarter and the number of quarters becomes 3 * 4 = 12.
the future value becomes 22796.55.

i used the financial calculator at https://arachnoid.com/finance/index.html

here are the results.
the first results give you the future value 16700 for 24 months at .233333.....% per month.
the second results give you the future value of 17660.73 for 12 quarters at 2.15% per quarter.





let me know if you have any questions.
theo

Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
Brooke invested $16,700 in a mutual fund at 2.8% compounded monthly.
After 2 years, the interest rate was changed to 8.6% compounded quarterly.
a) How much was the value of the fund 5 years after the rate change? $
b) How much was the total compound interest earned during the whole term?
~~~~~~~~~~~~~~~~ 

First two years (first term), the fund works according to this formula

    FV = 16700%2A%281%2B0.028%2F12%29%5E%282%2A12%29.


Next five years (the second term), the fund works according to this formula

    FV= A%2A%281%2B0.086%2F4%29%5E%285%2A4%29,


where A is the amount deposited at the second term.


Since the output from the first term is the input for the second term, you can combine the formulas
to calculate the answer after two terms in one formula

    FV = 16700%2A%28%281%2B0.028%2F12%29%5E%282%2A12%29%29%2A%28%281%2B0.086%2F4%29%5E%285%2A4%29%29.


After that, you can copy-paste this formula into a calculator which accepts formulas

(for example, Excel spreadsheet or online free of charge calculator www.desmos.com/calculator) and get the answer in one click.


ANSWER to question (a).  27025.64 dollars.


ANSWER to question (b)  is the difference $27025.64 - $16700 = $10325.64.

Solved.

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To see many other similar  (and different)  solved problems on compounded interest accounts,  look into the lesson
    - Compounded interest percentage problems
in this site.

Learn the subject from there.

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Be aware: calculations and the answer in the post by @Theo are incorrect.