Liberal Arts

Question

How much money should be invested now (rounded to the nearest cent), called the initial investment, in a State Bond investment that yields 9% per year, compounded monthly for 10 years, if you wish it to be worth $40,000 after 10 years?

Answer 1

Compounding n times per year: A = P(1+r/n)^nt where A is the desired future value $40,000, P is the principal to be invested (lump sum) for t years, annual compounding rate r, compounding n times/yr.

 

r = 9% = 0.09

n = 12

t = 10.

 

So P = A / (1+r/n)^nt

 

Substitute the values and do the calculation!  Check the answer for reasonableness(a.k.a. common sense).