Niles is making an investment with an expected return of 12 percent. if the standard deviation of the return is 4.5 percent, and if niles is investing $100,000, then what dollar amount is niles 90 percent sure that he will have at the end of the year? (do not round intermediate computations.)

$104,597.5

Explanation:

Given:

Expected return = 12%

Standard deviation on return = 4.5%

Amount invested = $100,000

Confidence level = 90%

Now,

For the 90% confidence level the z score is 1.645

Therefore,

the minimum percentage gain at the end of year will be

= mean(i.e the expected return) - (z × Standard deviation)

= 12% - 1.645 × 4.5%

= 12% - 7.4025%

= 4.5975%

Thus, 4.5975% of initial amount =

= $4,597.50

Hence,

Final amount = $100,000 + $4,597.50

= $104,597.5