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Future value.   A speculator has purchased land along the southern Oregon coast. He has taken a loan with the​ end-of-year payments of ​$7 comma 000 for 8 years. The loan rate is 5 ​%. At the end of 8 ​years, he believes that he can sell the land for ​$50 comma 000 . If he is correct on the future​ price, did he make a wise​ investment?

Respuesta :

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Answer: Not a wise investment as Cost exceeds Receipts.

Explanation:

As the amount is a constant payment, it is an annuity and as it is in future we are looking for the future value of an annuity:

Future Value of Annuity = Annuity * [ ( 1 + rate ) ^ time period - 1] / rate

= 7,000 * [ ( 1 + 5%)⁸ - 1] / 5%

= $66,843.76

Speculator pays $66,843.76 for loan and sells for $50,000.

The speculator would be paying more for the loan than they will sell the land for so this is not a wise investment.

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