Dieter deposits $9000 into an account that pays 10%/a compounded

quarterly. After three years, the interest rate changes to 9%/a compounded

semi-annually. Calculate the value of his investment two years after

this change. please include steps

For the first three years, the interest is 10%/a compounded quarterly

So after the first year (4 quarters), the value is 9000x(1+10%)^4=9000x1.1^4.

After the second year, the value is 9000x1.1^4x1.1^4=9000x1.1^8

After the third year, the value is 9000x1.1^8x1.1^4=9000x1.1^12.

Now the rate changes to 9%/a compounded semi-annually.

So one year after the change, the value is 9000x1.1^12x(1+9%)^2=9000x1.1^12x1.09^2

Two year after the change, the value is 9000x1.1^12x1.09^2x1.09^2=9000x1.1^12x1.09^4

So the investment becomes 9000x1.1^12x1.09^4=39871 dollars.

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