exponential functions?

Question

 

How much money will you need to invest initially to have $10,500.00 in two and one-quarter years if the money is compounded monthly at an annual rate of?

 

Answer 1

Formulas for Compound Interest :

After t years, the balance A in an account with principal P and annual interest rate r (in decimal form) is given by the following formulas.

1. For n compoundings per year : A = P ( 1 + r/n )^nt.

2. For continuous compounding: A = P e^rt.

Balance = A = 10,500.00 dollars,

For monthly compounding, = n = 12,

Annual interest rate (in decimal form) = r = 3 1/4 % = (12 + 1)/4 % = 13/4 % = 13/400 = 0.0325,

Time (years) = t = two and one - quaretr years = 2 1/4 years = [ {2(4) + 1}/4 ] years = [ (8 + 1)/4 ] years = 9/4 years,

Principle = P = ?.

For n compoundings per year : A = P ( 1 + r/n )^nt.

10,500.00 = P ( 1 + 0.0325/12 )^{(12) (9/4)}

10,500.00 ≅ P ( 1.00270833 )²⁷

10,500.00 ≅ P ( 1.075758673 )

(10,500.00) / (1.075758673) ≅ P

P ≅ 9,760.55 dollars.

The initial investment (principle) is 9,760.55 dollars.