Problema Solution
Ben Franklin's gift of 5,000 to New York grew to 10,000,000 in 200 years. At what interest rate compound annually would this growth occur?
Answer provided by our tutors
P = $5,000 the principal amount
r = annual interest rate as a decimal
t = 200 years number of years
A = $10,000,000 amount of money accumulated after t years, including interest
n = 1 number of times the interest is compounded per year
A = P(1 + r/n)^(nt)
10,000,000 = 5,000(1 + r/1)^(1*200)
5,000(1 + r)^200 = 10,000,000
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r = 0.0387 or 3.87%
This growth will occur at 3.87% annual interest rate compounded annually.