A bank offers a CD that pays a simple interest rate of $3.0 \%$. How much must you put in this CD now in order to have $\$ 5,000$ for a home-entertainment center in 5 years.
The present value that must be invested to get $\$ 5,000$ after 5 years at an interest rate of $3.0 \%$ is $\$ \square$. (Round up to the nearest cent.)
Answer
\(\boxed{4313.04}\) is the amount that must be invested now to have $5000 in 5 years at an annual simple interest rate of 3%
Step 1 ：We are given that the future value (FV) is $5000, the annual interest rate (r) is 3% or 0.03 in decimal form, and the time (t) is 5 years. The interest is simple and compounded once per year.
Step 2 ：We can calculate the present value (PV) using the formula: \(PV = \frac{FV}{(1 + r)^t}\)
Step 3 ：Substituting the given values into the formula, we get: \(PV = \frac{5000}{(1 + 0.03)^5}\)
Step 4 ：Calculating the above expression, we find that the present value (PV) is approximately $4313.04
Step 5 ：\(\boxed{4313.04}\) is the amount that must be invested now to have $5000 in 5 years at an annual simple interest rate of 3%
