An initial investment of 20000 is invested for 25yearsin an

An initial investment of $20,000 is invested for 2.5yearsin an account that earns 1.2% interest continuously compounded. The balance is then transferred to a certifcate of deposit that pays 2% interest, compounded quarterly, for a period of 1 year. What is the final value of the investment?

Solution

Initial Investment=$20000

For 2.5 years,the rate of interest is 1.2%,compounded continuously

As we know that the amount(A) for a principal (P) (which is the investement here) at a percentage rate (R ) for a time N(N is the number of years or quarters or half years as is the case ) in case of compound interest is given by the formula,

A=P*[1 + (R/100)]^N

So,the amount after 2.5 years=$ 20,000 *[1+(1.2/100)]^2.5

                                                =$20,000*[1.012]^2.5

                                                =$ 20,605.4107

In the same way the the final amount ,for the certificate,at a rate of 2% compounded quarterly for one year                      =$ 20,605.4107*[1+(2/100)]^4 {Since the rate is compounded quarterly and there are four quarters in an year so here N=4 }

=$ 20,605.4107*[1.02]^4

=$ 22,303.96

So the final value of investment= $ 22,303.96