Beth saves $2,500 a year from age 25 until age 34 (inclusive) and invests the money in an account earning ten percent annually. Beth stops investing at age 34 but does not withdraw the accumulation until age 65. In contrast, Bill saves $2,500 a year from age 35 until age 65 inclusively and invests in a similar account to Beth, earning ten percent annually. Because Bill saved significantly more than Beth, he will have accumulated significantly more than her at age 65.
True or False?

False

Bill will have less than Beth

Explanation:

let us compare the amounts accumulated by the two individuals at age 65 to see which is more.

Money accumulated by Bill at age 65:

Since bill saves $2500 a year for 30 years,  amount saved at the end of 30 years = 2500 X 30 = $75000.

Money accumulated by Beth at age 65:

Beth saves $2,500 a year from age 25 until age 34: Amount saved = 2500 X 9 = $22500

Invests the money in an account earning ten percent annually for 31 years.

Assuming it was at a simple interest rate,

The interest at the end of the 31st year will be:

Therefore total amount at age 65 = $22, 500 + 69750 = $92,250.

∴ This shows that Bill will have less money than Beth. Primarily due to the fact that he started investing at a lot later time than Beth.

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