Fractions word problem

Question

Michael Wittry has been investing in his Roth IRA retirement account for 17 years. Four years ago, his account was worth $215,652. After losing 1/4  of its original value, it then gained 1/3  of its new value back. What is the current value of his Roth IRA?

Answer 1

It's always best to use multiplicative factors rather than additive factors when doing these calculations.

Reinterpret a loss of 1/4 as a multiplier of 3/4 and a gain of 1/3 as a multiplier of 4/3.

Then you can take the V₁ (3/4)(4/3) = V₂ combining the two multiplicative steps

which shows that the final value is the same as the initial value.

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