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Mariam has just won some money on a game show. She has the option to take a lump sum payment of $625,000 now or get paid an annuity of $4500 per month for the next 15 years. Assuming the growth rate of the economy is 3.3% compounded annually over the next 15 years, which is the better deal for Marion and by how much?

User Aguilarpgc
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1 Answer

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Final answer:

To determine the better option for Mariam, the lump sum of $625,000 is compared to the future value of a $4,500 monthly annuity over 15 years with a 3.3% annual compound growth rate. The future value of the annuity is calculated, and whichever amount is higher indicates the better deal by showing the difference between the two.

Step-by-step explanation:

To determine which option is better for Mariam, we will compare the lump sum payment of $625,000 to the future value of the annuity of $4,500 per month for the next 15 years. We will need to take into account the growth rate of the economy of 3.3% compounded annually.

Firstly, the annuity needs to be converted to an equivalent annual amount:

  • $4,500 × 12 months = $54,000 per year.

Next, we calculate the future value of the annuity using the formula for the future value of an annuity:

Future Value = P × {[(1 + r)^n - 1] / r}

Where:

  • P is the periodic payment,
  • r is the interest rate per period, and
  • n is the number of periods.

For Mariam's case:

  • P = $54,000
  • r = 0.033 (3.3% expressed as a decimal)
  • n = 15 years

Plugging these values into the formula:

Future Value = $54,000 × {[(1 + 0.033)^15 - 1] / 0.033}

After calculating, we compare this future value to the $625,000 lump sum to see which is higher. If the future value of the annuity is greater than $625,000, then the annuity is the better deal for Mariam; otherwise, the lump sum is preferable. We also calculate the difference between the two amounts to see how much better the chosen option is.

User AdibP
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