A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born in order to have $43,000 when the child reaches the age of 18? Assume the money earns 7% interest, compounded quarterly. (Round your answer to two decimal places.)

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Asked Oct 28, 2019
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A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born in order to have $43,000 when the child reaches the age of 18? Assume the money earns 7% interest, compounded quarterly. (Round your answer to two decimal places.)

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Expert Answer

Step 1

Present value can be defined as the amount which is to be set aside in order to have a pre-defined sum at a future date at given interest rate.

It is given that,

Future value is $43,000.

Interest rate is 7% compounded quarterly. So, interest rate per quarter will be (7% ÷ 4) = 1.75%.

Number of years is 18. So, total number of periods will be 18 × 4 = 72.

Step 2

The formula to calculate present value is given below:

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Future value Present value (1+) Here, i is interest rate nis number of periods

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Step 3

Substitute $43,000 for future value, 1.75% f...

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$43,000 Present value (1+1.75%) $43,000 1.01757 $43,000 3.4872 =$12,330.77

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