Raymond B. answered • 02/25/20

Math, microeconomics or criminal justice

This question has "Simple interest" written above it, as if you do not compound the interest.

With just simple interest, you earn $3 for each $100 invested, per year, or $6 per two years. Every two years your $100 earns $6. if you want to earn $10,000, divide $6 into $10,000 to get 1,666.66. Multiply that by $100 to get $166,666.66 as the needed investment.

But if you compounded interest, less is needed

Assuming 3% means annual interest rate, compounded annually, the general formula with r=interest rate of 3% and t = number of years = 2

is A=P(1+r)^{t} = P(1+.03)^{2} = P(1.03)^{2} = P(1.0609) P=A/1.0609 = (P+10,000)/1.0609 solve for P, the investment that gets you $10,000 in interest. A=P+10,000 = the amount invested + interest earned

1.0609P=P+10,000

0.0609P = 10,000

P=10,000/0.0609 = $164,203.61, slightly less than if it were only simple interest, about $2,4463.05 less investment required.