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Inessa05 [86]
3 years ago
14

Help please with this question

Mathematics
1 answer:
choli [55]3 years ago
7 0

Answer:

They lose about 2.79% in purchasing power.

Step-by-step explanation:

Whenever you're dealing with purchasing power and inflation, you need to carefully define what the reference is for any changes you might be talking about. Here, we take <em>purchasing power at the beginning of the year</em> as the reference. Since we don't know when the 6% year occurred relative to the year in which the saving balance was $200,000, we choose to deal primarily with percentages, rather than dollar amounts.

Each day, the account value is multiplied by (1 + 0.03/365), so at the end of the year the value is multiplied by about

... (1 +0.03/365)^365 ≈ 1.03045326

Something that had a cost of 1 at the beginning of the year will have a cost of 1.06 at the end of the year. A savings account value of 1 at the beginning of the year would purchase one whole item. At the end of the year, the value of the savings account will purchase ...

... 1.03045326 / 1.06 ≈ 0.9721 . . . items

That is, the loss of purchasing power is about ...

... 1 - 0.9721 = 2.79%

_____

If the account value is $200,000 at the beginning of the year in question, then the purchasing power <em>normalized to what it was at the beginning of the year</em> is now $194,425.14, about $5,574.85 less.

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