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Linda Roy received a $205,000 inheritance after taxes from her parents. She invested it at 6.5%...

Linda Roy received a $205,000 inheritance after taxes from her parents. She invested it at 6.5% interest compounded quarterly for 8 years. A year later, she sold one of her rental properties for $215,000 and invested that money at 5.5% compounded semiannually for 7 years. Both of the investments have matured. She is hoping to have at least $505,000 in 12 years compounded annually at 4.5% interest so she can move to Hawaii.

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Expert Solution

Part 1)

The future value of inheritance investment is calculated as follows:

Future Value of Inheritance Investment = Amount Received as Inheritance*(1+Investment Rate/Number of Compoundings in a Year)^ Period

Here, Amount Received as Inheritance = $205,000, Investment Rate = 6.5%, Number of Compoundings in a Year = 4, and Period = Years*Number of Compoundings in a Year = 8*4 = 32

Substituting these values in the above formula, we get,

Future Value of Inheritance Investment = 205,000*(1+6.5%/4)^32 = $343,377.42 (answer for Part 1)

______

Part 2)

The future value of rental property investment is determined as below:

Future Value of Rental Property Investment = Amount Received from Sale of Rental Property*(1+Investment Rate/Number of Compoundings in a Year)^ Period

Here, Amount Received from Sale of Rental Property = $215,000, Investment Rate = 5.5%, Number of Compoundings in a Year = 2, and Period = Years*Number of Compoundings in a Year = 7*2 = 14

Substituting these values in the above formula, we get,

Future Value of Rental Property Investment = 215,000*(1+5.5%/2)^14 = $314,328.74 (answer for Part 2)

______

Part 3)

The present value of final investment is derived as follows:

Present Value of Final Investment = Amount Desired after 12 Years/(1+Interest Rate)^Years

Here, Amount Desired after 12 Years = $505,000, Interest Rate = 4.5% and Years = 12

Substituting these values in the above formula, we get,

Present Value of Final Investment = (505,000)/(1+4.5%)^12 = $297,780.25 (answer for Part 3)

______

Part 4)

The future value of final investment is calculated as below:

Future Value of Final Investment = (Future Value of Inheritance Investment + Future Value of Rental Property Investment)*(1+Interest Rate)^Years = 343,377.42 + 314,328.74 = 657,706.15*(1+4.5%)^12 = $1,115,391.66 (answer for Part 4)

______

Part 5)

Yes, Linda will meet her goal as the future value of final investment exceeds the value of $505,000 needed after 12 years.

jeff jeffy answered 1 year ago
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