Question

Asa has invested money from the settlement of an insurance claim. She plans to withdraw $2,600 from her savings account at the end of each quarter for four years. If the payments are deferred for eight years and interest is 5% compounded annually, what was the amount of the insurance settlement? The insurance settlement was $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

Asa is looking to find the present value of an annuity due with quarterly payments using a 5% annual compounded interest rate. To solve this, the present value of each deferred payment has to be calculated and then summed up to find the initial settlement amount. The solution will reveal the insurance settlement Asa received to cover the future withdrawals.

Step-by-step explanation:

Asa is dealing with a financial problem that requires understanding of compound interest and present value of annuities. Since Asa plans to withdraw $2,600 at the end of each quarter for four years, we have 4 quarters per year multiplied by 4 years, for a total of 16 payments. With an interest rate of 5% compounded annually, and the payments deferred for eight years, we can calculate the present value of an annuity due to determine the insurance settlement amount.

To find the present value of these payments, we must discount each payment back to the present value. The present value of each payment is found using the formula PV = P / (1 + r)^n, where P is the payment amount, r is the interest rate per period, and n is the number of periods.

For the insurance settlement, we need to find the sum of the present values of all deferred payments. Once calculated, this sum will represent the amount of money that should have been invested initially to satisfy the future withdrawals. The final settlement amount will be the sum of these present values rounded to the nearest cent as required.