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.