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Calculate the present worth of $53.000 to be received 6 years from now, if the predicted real rate of return is 15% per year and the inflation rate is 8% per year.

User Yanwar Sky
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5 votes

Answer:

$13,627.33

Step-by-step explanation:

To account for the effect of inflation, we need to bring the future value of $53,000 back to present day value. We can use the formula for the future value adjusted for inflation:

FV_inflation = FV_nominal / (1 + inflation_rate)^n

Where:

FV_inflation is the future value adjusted for inflation

FV_nominal is the nominal future value ($53,000 in this case)

inflation_rate is the annual inflation rate (8% per year)

n is the number of years (6 years in this case)

FV_inflation = $53,000 / (1 + 0.08)^6

FV_inflation = $53,000 / (1.08)^6

FV_inflation = $53,000 / 1.593848

FV_inflation ≈ $33,263.81

The adjusted future value after accounting for inflation is approximately $33,263.81.

Adjust for real rate of return:

Now, we need to discount the adjusted future value to the present value based on the predicted real rate of return. We can use the formula for the present value of a future amount:

PV = FV / (1 + real_rate)^n

Where:

PV is the present value we want to calculate

FV is the adjusted future value after accounting for inflation ($33,263.81)

real_rate is the predicted real rate of return (15% per year)

n is the number of years (6 years in this case)

PV = $33,263.81 / (1 + 0.15)^6

PV = $33,263.81 / (1.15)^6

PV = $33,263.81 / 2.4414

PV ≈ $13,627.33

Therefore, the present worth of $53,000 to be received 6 years from now, considering a predicted real rate of return of 15% per year and an inflation rate of 8% per year, is approximately $13,627.33.

User Alejandro Gonzalez
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