Question

Your employer has given you the following task:

He wants to know how much he has to invest now to have $10,000 for a new piece of machinery he wants to purchase in 5 years. The bank has quoted him an interest rate of 8% compounded semi-annually

How much to invest (round your answer to two decimals).

Answer 1

To have $10,000 in 5 years with an 8% interest rate compounded semi-annually, one would need to invest $6755.94 now.

Step-by-step explanation:

To determine how much needs to be invested now to have $10,000 in 5 years with an interest rate of 8% compounded semi-annually, we use the present value formula for compound interest:

PV = FV / (1 + r/n)nt

Where:

• PV = Present Value (amount of money to be invested now)
• FV = Future Value (the amount of money we want to have in the future, which is $10,000)
• r = annual interest rate (8% or 0.08)
• n = number of times the interest is compounded per year (semi-annually means n=2)
• t = number of years the money is invested (5 years)

Using these values, we calculate:

PV = $10,000 / (1 + 0.08/2)2*5

PV = $10,000 / (1 + 0.04)10

PV = $10,000 / (1.04)10

PV = $10,000 / 1.48024

PV = $6755.94

Therefore, you need to invest $6755.94 now to have $10,000 for the new piece of machinery in 5 years, assuming an 8% interest rate compounded semi-annually.