Ben franklin's gift of $8000 to New York City grew to 5000000 in 200 years. At what interest rate compounded annually would this growth occur?

Question

 Ben franklin's gift of $8000 to New York City grew to 5000000 in 200 years. At what interest rate compounded annually would this growth occur?

Answer 1

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 = 625^1/200

 

r = 625^1/200 - 1 = 0.0327

 

r ≅ 3.27%