Ben franklin's gift of $2,000 to New York City grew to 9,000,000 in 200 years. At what interest rate compounded annually would this growth occur?

r ≅ 3.27% : d

We need to use the compound interest formula where the future amount is determined by

A = P (1 + r/n) nt

A = future or present amount = 5,000,000

P = initial amount invested = 8,000

r = interest rate as a decimal (to be determined)

n = # times compounded in a year = 1

t = # years = 200

5000000 = 8000 (1+r/1) 1 (200) = 8000 (1+r) 200

(1+r) 200 = 5,000,000/8,000

(1+r) 200 = 625

1+r = 200√625

1 + r = 6251/200

r = 6251/200 - 1 = 0.0327

r ≅ 3.27%