Given a quarterly effective interest rate of 4% an investment of X today and another of...

Given a quarterly effective interest rate of 4% an investment of X today and another of 7X at the end of 2 years will amount to $19, 470.04 four years from today. Find X. Remember to first express the equation of value, then and X.

Expert Solution

Quarterly effective interest rate (i) = 4%

Future Value = Present value * (1+i)ⁿ

Therefore Value of investment after 4 years made now = Present value * (1+i)ⁿ

Therefore Value of investment after 4 years made now = X * (1+0.04)¹⁶

{4 years = 16 quarters}

Therefore Value of investment after 4 years made now = X * (1+0.04)¹⁶

Therefore Value of investment after 4 years made now = 1.872981X

Therefore Value of investment made 2 years from now after 4 years = Present value * (1+i)ⁿ

Therefore Value of investment made 2 years from now after 4 years = X * (1+0.04)⁸

{2 years = 8 quarters}

Therefore Value of investment made 2 years from now after 4 years = X * (1+0.04)⁸

Therefore Value of investment made 2 years from now after 4 years = 1.368569X

Therefore Future value of investments made = 1.872981X + 1.368569X

19470.04 = 3.24155X

Therefore X = $6006.40

jeff jeffy answered 2 years ago

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