Question

Asa has invested money from the settlement of an insurance claim. She plans to withdraw ​$5360 from her savings account at the end of each 6 months for 5 years. If the payments are deferred for 3 years and interest is ​6% compounded quarterly​, what was the amount of the insurance​ settlement?

Answer 1

To find the amount of the insurance settlement, calculate the present value of an annuity with semi-annual payments of $5360 for 5 years, deferred for 3 years, with a 6% interest rate compounded quarterly.

Step-by-step explanation:

To determine the initial amount of the insurance settlement Asa invested, we need to calculate the present value of an annuity due to the deferral of withdrawals for 3 years. The payments of $5360 are made semi-annually for 5 years, with the first withdrawal happening 3 years from the initial investment. We must also account for the quarterly compounded interest at a rate of 6%.

Given the information, we use the formula for the present value of an annuity. Since interest is compounded quarterly, we must adjust the interest rate and the number of payments accordingly. However, the provided example formulas relate to annual compounding; we must therefore adjust them to quarterly compounding. A financial calculator or appropriate software is typically used to find the present value in such compound interest problems.