Ben Franklin gift of $10,000 to NYC grew to $10,000,00 in 200 years. At what interest rate compounded annually would this growth occur

Question

Need help solving this problem.

Answer 1

Compound interest:  A = P(1+r/n)^nt

A = future amount = 10,000,000

P = principal investment = 10,000

r = interest rate as a decimal

n = # times compounded per year = 1

t = time in years = 200

 

10000000 = 10000(1+r/1)¹⁽²⁰⁰⁾

1000 = (1+r)²⁰⁰

²⁰⁰√1000 = 1+r

r = ²⁰⁰√1000 - 1

r = .0351

 

Interest rate is 3.5%

Answer 2

10,000,000 = 10,000(1 + r)²⁰⁰

 

1000 = (1+r)²⁰⁰

 

1000^(1/200) = 1 + r

 

r = 1000^(1/200) - 1 =.0351