exponential functions?

Question

Calculate the future value of $1,000,000.00, earning interest at a rate of 3% that is compounded quarterly for 4 years and 3 months.

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.

Principle = P = 1,000,000.00 dollars,

Compoundings per year = n = 4,

Annual interest rate (in decimal form) = r = 3% = 3/100 = 0.03,

Time (years) = t = 4 years and 3 months = [ 4 + 3/12 ] years = [ 4 + 1/4 ] years = [ (16 + 1)/4 ] years = 17/4 years,

Balance = A = ?.

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

A = (1,000,000)( 1 + 0.03/4 )^{(4) (17/4)}

A = (1,000,000)( 1.0075 )¹⁷

A ≅ (1,000,000)( 1.1354445545 )

A ≅ 1135444.5545 dollars.

The total amount in future is 1,135,444.55 dollars.