If 46400 dollars is invested at an interest rate of 9 percent per year, compounded semiannually, find the value of the investment after the given number of years.

5,10,15 years

Question

If 46400 dollars is invested at an interest rate of 9 percent per year, compounded semiannually, find the value of the investment after the given number of years.

5,10,15 years

anonymous · Answer

$$P(t) = P _{0} (1+r)^{t}$$P(t) is the total amount of the investment at time t (in this problem, t is in steps of 6 months: semianually), P0 is the initial investment, and r is the interest rate (expressed as a decimal, and for the time period of 1t).

Since t=6 months, then the values you're interested in are 10, 20, and 30.  And, since it's half a year, you are really getting 4.5% every 6 months, so r=4.5%, or r=0.045.  The rest is just plugging the values into the equation and using a calculator.

anonymous · Answer

As a check, without just giving you the answers, the value of the investment after 2.5 years is $57, 822.84.