Problema Solution

Fred invests $25,000 in a certificate of deposit (CD) earning 4.8% interest compunded quarterly. How much this CD is worth in 5 years and in 10 years? Find the exponententional functional, then evaluate.

Answer provided by our tutors

Let t = # of years since the initial investment in the CD.  Since interest is compounded quarterly, then the interest will be compounded four times per year.  This means our function will look something like: P(t) = P*(1.048)4t, where P is the initial investment.  The exponential base is 1.048, which corresponds to the 4.8% interest rate offered on the CD.  The exponent is 4t, which corresponds to the quarterly (four times per year) compounding of interest.  In general, if we are offered an x% interest rate, our exponential base will be 1 + (x/100).  In this particular case, P = $25,000 and so we have P(t) = 25000*(1.048)4t.

So, after 5 years, the CD is worth P(5) = 25000*(1.048)20.

After 10 years, the CD is worth P(10) = 25000*(1.048)40.