Question

How much money should be invested today in order to have $8340 at the end of 9 years if the interest paid is a nominal rate of 4.25 percent compounded semi-annually?

Answer 1

Amount to be invested today is the present value of $8,340 receivable 9 years from now discounted at required rate of return

When interest is compounded semi-annually, interest rate is divided by 2 and time period is multiplied by 2

So, applicable interest rate

= 4.25 / 2

= 2.125%

Time period = 9 x 2 = 18 half years

So, present value factor

= 1 / (1 + rate of discounting) ^ number of periods

= 1 / (1+2.125/100)^18

= 1 / 1.460082

= 0.684893

So, amount to be invested today

= Future value x Present value factor

= $8,340 x 0.684893

= $5,712.01