How much should Kevin deposit annually to buy a yacht costing $450,000 in 20 years with a 2% inflation rate?

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Multiple Choice

How much should Kevin deposit annually to buy a yacht costing $450,000 in 20 years with a 2% inflation rate?

To determine how much Kevin should deposit annually to buy a yacht costing $450,000 in 20 years while accounting for a 2% inflation rate, it's essential first to adjust the future cost of the yacht for inflation. After 20 years with a 2% inflation rate, the future value of the yacht can be calculated using the formula for future value considering inflation: \[ \text{Future Cost} = \text{Current Cost} \times (1 + \text{Inflation Rate})^\text{Number of Years} \] Substituting the values: \[ \text{Future Cost} = 450,000 \times (1 + 0.02)^{20} \] Calculating this gives: \[ \text{Future Cost} \approx 450,000 \times 1.485947 \approx 667,676.50 \] Now, Kevin wants to save to reach this future value. If he makes equal annual deposits, we can use the future value of an annuity formula to determine the amount he needs to save each year: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) is

To determine how much Kevin should deposit annually to buy a yacht costing $450,000 in 20 years while accounting for a 2% inflation rate, it's essential first to adjust the future cost of the yacht for inflation.

After 20 years with a 2% inflation rate, the future value of the yacht can be calculated using the formula for future value considering inflation:

[ \text{Future Cost} = \text{Current Cost} \times (1 + \text{Inflation Rate})^\text{Number of Years} ]

Substituting the values:

[ \text{Future Cost} = 450,000 \times (1 + 0.02)^{20} ]

Calculating this gives:

[ \text{Future Cost} \approx 450,000 \times 1.485947 \approx 667,676.50 ]

Now, Kevin wants to save to reach this future value. If he makes equal annual deposits, we can use the future value of an annuity formula to determine the amount he needs to save each year:

[ FV = P \times \frac{(1 + r)^n - 1}{r} ]

Where:

  • ( FV ) is
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