Final answer:
To find the future value of 93 pence in a savings account at 2.5% interest compounded annually for 100 years, we use the formula Future Value = Principal × (1 + Interest Rate per Period)^Number of Periods. After computing this, we can determine the total amount available after 100 years.
Step-by-step explanation:
To calculate the future value of a sum of money in a savings account with compound interest, we use the compound interest formula:
Future Value = Principal × (1 + Interest Rate per Period)^Number of Periods
In this case, the principal is 93 pence, the interest rate per annum is 2.5%, and the period is 100 years. Therefore, we need to plug in the values into the formula:
Future Value = 0.93 × (1 + 0.025)^100
Calculating this gives us:
Future Value = 0.93 × (1.025)^100
=10.9867 pence
the total amount.
It is important to note that the actual value can significantly change depending on factors such as taxes, fees, or changes in the interest rate over time, but this calculation gives a theoretical amount based on a constant rate.