Each granddaughter is entitled to a certain amount with compound interest, depending on the given interest rate. With a 3% interest rate, each granddaughter is entitled to $1181.64. With a 6% interest rate, each granddaughter is entitled to $6493.86.
To calculate the amount each granddaughter is entitled to with compound interest, we can use the formula:
Future Value = Principal + Principal n * (1 + Interest Rate)n
where:
- Principal = $100
- n = number of years (1994 - 1880 = 114 years)
- Interest Rate = given interest rate (3% or 6%)
a. For an interest rate of 3%:
Future Value = $100 + $100 * (1 + 0.03)114
Calculating this value gives us $1181.64. Therefore, each granddaughter is entitled to $1181.64 with 3% interest.
b. For an interest rate of 6%:
Future Value = $100 + $100 * (1 + 0.06)114
Calculating this value gives us $6493.86. Therefore, each granddaughter is entitled to $6493.86 with 6% interest.
Complete Question :
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% ?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.