Question

James bennett also allocates wealth between youth and old age. He has no cash currently (in his youth), but will inherit $3000 in his old age. He can lend and borrow at the bank at 18% (that is, lending $1 in youth will give him $1. 18 in old age). He has an investment opportunity that costs $12,000 now in his youth and has a payoff of $15,000 in his old age. This is the only investment opportunity available to him. What is the most he can consume in his youth?.

Answer 1

The present value (PV) of $15,254.24 is the most James bennett can consume in his youth.

Given the following data:

• Inheritance = $3000

• Interest rate = 18%

• Investment opportunity (youth) = $12,000

• Investment opportunity (old age) = $15,000

To calculate the most James bennett can consume in his youth:

First of all, we would determine the future value of James bennett from his investment and inheritance as follows:

$FV = 15000 + 3000$

FV = $18000

Mathematically, the most James bennett can consume in his youth is given by this formula:

$PV = \frac{FV}{(1+i)^n}$

Substituting the given parameters into the formula, we have;

$PV = \frac{18000}{(1+0.18)^1}\\\\PV = \frac{18000}{1.18}$

PV = $15,254.24

Therefore, the present value (PV) of $15,254.24 is the most James bennett can consume in his youth.

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