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Alice deposits $2000 at time 0 under a nominal interest rate 6% compounded monthly for two years. And the end of the first year she deposit another $3000 under a nominal interest rate 7% compounded quarterly for one year. What is the equivalent annual effective interest rate for these two deposits over the first two years (i.e. the rate under which Alice would have the same total balance at time 2)

Respuesta :

TomShelby

Answer:

effective rate of 6.59%

Explanation:

First, we solve for the amount after 2-years

[tex]2,000 \times (1 +\frac{0.06}{12}) ^{2 \times 12})+ 3,000 (1+\frac{0.07}{4})^4=[/tex]

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 2,000.00

time 24.00

rate 0.00500

[tex]2000 \: (1+ 0.005)^{24} = Amount[/tex]

Amount 2,254.32

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 3,000.00

time 4.00

rate 0.01750

[tex]3000 \: (1+ 0.0175)^{4} = Amount[/tex]

Amount 3,215.58

Total: 2,254.32 + 3,215.58 = 5,469.90

Now, we solve for the effective rate:

[tex]2,000(1+r_e)^2 + 3,000(1+r_e) - 5,469.90 = 0[/tex]

We use the quadratic formula and find the roots:

2.5658882124183746

1.0658882124183746

we use the positive one.

Getting an effective rae of 6.59%

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