Final answer:
To determine the fixed annual deposit required for ABC Company to meet its future payment obligations at an 8% annual interest rate, we must calculate the present value of each future payment and sum them up, then use the future value of a series formula to solve for the annual deposit amount.
Step-by-step explanation:
To find out the fixed amount of money ABC Company should set aside each year to make the specified payments at an 8% interest rate, compounded annually, we need to calculate the present value of each payment and then determine the annual deposit required to accumulate the total present value over 5 years.
First, let's calculate the present value (PV) of each payment using the formula PV = P / (1 + r)^n, where P is the future payment, r is the annual interest rate, and n is the number of years until payment. Here are the calculations:
- PV of $10,000 paid immediately = $10,000 (since no time to accumulate interest)
- PV of $1,000 paid at the end of year 1 = $1,000 / (1 + 0.08)^1
- PV of $1,500 paid at the end of year 2 = $1,500 / (1 + 0.08)^2
- PV of $2,000 paid at the end of year 3 = $2,000 / (1 + 0.08)^3
- PV of $2,500 paid at the end of year 4 = $2,500 / (1 + 0.08)^4
- PV of $3,000 paid at the end of year 5 = $3,000 / (1 + 0.08)^5
Once we have the present values, we sum them up to get the total present value that needs to be funded by equal annual deposits. Then, we use the future value of a series formula FV = PMT × ((1 + r)^t - 1) / r to solve for PMT, the fixed annual payment. Here, FV is the total present value, r is the annual interest rate, t is the number of years, and PMT is the fixed amount the company needs to set aside.
Through these calculations, we find out the fixed amount that ABC Company should plan to set aside each year at an 8% interest rate to make the above payments.