Question on Calculating Compound Interest

Topic : Compound Interest

Question : Need to determine the number of parts that would have to be produced per year for 10 years to generate the same amount of money that would be made if the $500,000 were invested at 5% compund interest for 10 years.
Assume that the selling price of the part and cost to produce the part remain steady for the 10-year period.
It takes an hour to make 50 parts.
Every 50 parts made the company is bringing in $1675 after spending $825 in cost.

Answer :
Amount = P ( 1+ r) ^ 10 (assumed that the interest is compounded annually )
= 500000( 1+ .05) ^ 10 = $ 814447
given that : for $850, we need 1 hr ( 50 parts)
for $ 814447 , we need 814447 / 850 = 958.2 hrs ( in 10 years)
in 10 years we need 958.2 hrs , in 1 year we need 95.82 hrs
hence in one year, 95.82 ( 50 ) = 4791 parts have to be produced.
This can be done in this way too:
for $850 , 50 parts to be produced
for$ 814447 ; 50 ( 814447 ) / 850 = 47908 parts must be produced
in 1 year, 47908/10 = 4791 parts must be produced.

Hope any of the method will help you to solve compound interest questions.