Final answer:
The future value of Jack and Jil's savings with the Up-the-Hill Bank cannot be calculated without the specific interest rate. However, using a hypothetical 5% interest rate, the future savings can be estimated using the compound interest formula. Without knowing the interest rate or the amount saved after 10 years, it's uncertain if their savings would cover a $600 medical bill.
Step-by-step explanation:
Jack and Jil are saving for a rainy day by placing $45 in their local bank annually for 20 years, with the bank offering interest on their account. The future value of their savings can be determined using the formula of compound interest. This formula is based on the principle that interest is added to the principal amount (the original sum of money) as well as on the interest accumulated over the years.
However, the interest rate (fils) provided by the Up-the-Hill Bank is not specified in the question. To calculate the future value accurately, the specific interest rate would be needed. Without this critical piece of information, the exact future value at the end of 20 years cannot be determined.
If we assume an interest rate, for illustrative purposes, say 5% compounded annually, the future value (FV) of their savings would be calculated as follows: FV = P × (1 + r)^n, where P is the annual deposit ($45), r is the annual interest rate (0.05), and n is the number of years (20). The calculation would give us the amount Jack and Jil would have after 20 years.
Addressing part b of the question, with an accident occurring after 10 years, the savings they would have accumulated till then (without considering any withdrawals and assuming the same illustrative interest rate) would also be determined using the compound interest formula for 10 years. If the principal and interest accumulate to or exceed $600, it will be sufficient to cover the medical expenses.