Assume Eric Sanchez saves $100 a month by using coupons and doing comparison shopping. What is the annual savings amount? What would be the future value of this annual amount over 8 years, assuming an interest rate of 8 percent? (Exhibit 1-A, Exhibit 1-B, Exhibit 1-C, Exhibit 1-D) Note: Use appropriate factor(s) from the tables provided. Round time value factor to 3 decimal places and final answers to 2 decimal places.
Answer (1)
To calculate the annual savings and future value of these savings, follow these steps:
Calculate the Annual Savings : Eric saves $100 a month. Therefore, his annual savings would be: Annual Savings = 100 × 12 = $1200
Future Value of Annual Savings : To find the future value of these savings over 8 years at an 8% interest rate, we use the Future Value of an Annuity formula: F V = P × ( r ( 1 + r ) n − 1 ) Where:
P is the annual savings ($1200)
r is the annual interest rate (8% or 0.08)
n is the number of years (8)
Substitute the Values : F V = 1200 × ( 0.08 ( 1 + 0.08 ) 8 − 1 ) Using the future value annuity factor table (if available) to find the factor for 8% over 8 years, let's assume from the tables we get a factor of approximately 9.549: F V = 1200 × 9.549 = $11458.80
Therefore, the future value of Eric's savings over 8 years at an 8% interest rate is approximately $11,458.80.
