In 1880, five aboriginal trackers were each promised the equivalent of 100 Australian dollars for helping to capture the notorious outlaw Ned Kelley. In 1994, the granddaughters of two of the trackers claimed that this reward had not been paid. The Victorian prime minister stated that if this was true, the government would be happy to pay the $100. However, the granddaughters also claimed that they were entitled to compound interest.
a. How much was each granddaughter entitled to if the interest rate was 3%?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
b. How much was each entitled to if the interest rate was 6%?
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a. Using a 3% interest rate, we can calculate the amount each granddaughter is entitled to by compounding the interest of $100 for 114 years (1994-1880).
Principal = $100
Interest rate = 3%
Time = 114 years
Amount = Principal * (1 + (interest rate/100))^time
Amount = $100 * (1 + 0.03)^114
Amount = $100 * (1.03)^114
Amount ≈ $1480.85
Each granddaughter would be entitled to approximately $1480.85 if the interest rate was 3%.
b. Using a 6% interest rate, we can calculate the amount each granddaughter is entitled to by compounding the interest of $100 for 114 years.
Principal = $100
Interest rate = 6%
Time = 114 years
Amount = Principal * (1 + (interest rate/100))^time
Amount = $100 * (1 + 0.06)^114
Amount = $100 * (1.06)^114
Amount ≈ $1,792,716.80
Each granddaughter would be entitled to approximately $1,792,716.80 if the interest rate was 6%.
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