In 2010 a man mailed a $400 check to another man to repay a $400 debt of his great great grandfather who died in 1849. A bank estimated interest on the loan to be $454 million dollars for the 155 years it was due. Find the interest rate the bank was using assuming the interest is compounded annually.

9.41%

Step-by-step explanation:

Data provided in the question:

Present value of the debt = $400

Interest = $454 million = $454,000,000

Time, n = 155 years

Now,

Future value = Present value of the debt + Interest

or

Future value = $400 + $454,000,000

or

Future value = $454,000,400

Also,

Using the compounding formula,

Future value = Present value * (1 + r) ⁿ

here,

r is the interest rate

Thus,

$454,000,400 = $400 * (1 + r) ¹⁵⁵

or

(1 + r) ¹⁵⁵ = $454,000,400 : $400

(1 + r) ¹⁵⁵ = 1,135,001

or

1 + r = 1.0941

or

r = 1.0941 - 1

or

r = 0.0941

or

r = 0.0941 * 100% = 9.41%