Your grandmother has told you she can either give you $4,000 now or $5,000 when you graduate from college in three years.Your savings account earns 7% interest,compounded annually.Which option would be worth more to you now,and how much more? (Future Value of $1,Present Value of $1,Future Value Annuity of $1,Present Value Annuity of $1. )(Use appropriate factor from the PV tables.Round your final answer to 2 decimal places. )

Question

Quizplus · Accepted Answer

To determine which option is worth more, we calculate the present value (PV) of the $5,000 to be received in three years. Using the formula for PV: $PV = \frac{FV}{(1 + r)^n}$, where FV is the future value, r is the annual interest rate, and n is the number of years. With FV = $5,000, r = 7% or 0.07, and n = 3, the calculation is $PV = \frac{5000}{(1 + 0.07)^3}$. This gives us $PV = \frac{5000}{1.225043}$ or approximately $4081.50. Therefore, the present value of $5,000 received in three years is $4081.50, which is $81.50 more than the $4,000 received now.

Your Grandmother Has Told You She Can Either Give You