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If the interest rate is 4 percent, then you would be equally happy if you received a gift of either $100 today or a gift ofGroup of answer choices$110.00 two years from today.$112.49 three years from today.$116.00 four years from today.$123.67 five years from today.

Question

If the interest rate is 4 percent, then you would be equally happy if you received a gift of either 100todayoragiftofGroupofanswerchoices100 today or a gift ofGroup of answer choices110.00 two years from today.112.49threeyearsfromtoday.112.49 three years from today.116.00 four years from today.$123.67 five years from today.

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Solution

The question is asking which future gift amount would be equivalent to receiving $100 today given an annual interest rate of 4%. This is a question of calculating the future value of a present sum of money.

The formula for future value is FV = PV * (1 + r)^n, where:

  • FV is the future value of the money
  • PV is the present value of the money
  • r is the interest rate
  • n is the number of years

We can rearrange this formula to solve for PV: PV = FV / (1 + r)^n

Let's calculate the present value for each of the future gift amounts:

  1. 110.00twoyearsfromtoday:PV=110/(1+0.04)2=110.00 two years from today: PV = 110 / (1 + 0.04)^2 = 101.44
  2. 112.49threeyearsfromtoday:PV=112.49/(1+0.04)3=112.49 three years from today: PV = 112.49 / (1 + 0.04)^3 = 100.00
  3. 116.00fouryearsfromtoday:PV=116/(1+0.04)4=116.00 four years from today: PV = 116 / (1 + 0.04)^4 = 99.59
  4. 123.67fiveyearsfromtoday:PV=123.67/(1+0.04)5=123.67 five years from today: PV = 123.67 / (1 + 0.04)^5 = 100.00

So, given a 4% interest rate, you would be equally happy receiving 100todayor100 today or 112.49 three years from today or 123.67fiveyearsfromtoday,astheyallhavethesamepresentvalueof123.67 five years from today, as they all have the same present value of 100.

This problem has been solved

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