Money is invested in a savings account with a nominal interest rate of 2.4% conv

Question

Money is invested in a savings account with a nominal interest rate of 2.4% convertible monthly for three years. The rate of inflation is 1.5% for the first year, 2.8% for the second year, and 3.4% for the third year. Find the percentage of purchasing power lost during the time the money is invested; that is, find p so that if you could purchase exactly u units at the time the money was invested, three years later you could purchase u(1-.01p).

The answer is .40024%, I just don't know how to do it.

Explanation / Answer

The price of same unit after three years will be 1.078896, and the value of investment made in savings account will be 1.074578. Thus, the money value lost is 0.4318%, and this is 0.4002% of the price. Therefore, the lost in purchasing power is 0.4002%.

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