Problem 5.3 Your birthday is coming up and instead of other presents, your parents promised to give you $2,600 in cash. Since yo

Question

3 years ago

8

Problem 5.3 Your birthday is coming up and instead of other presents, your parents promised to give you $2,600 in cash. Since yo

u have a part-time job and, thus, don’t need the cash immediately, you decide to invest the money in a bank CD that pays an annual rate of 9.80 percent, compounded quarterly, for the next two years. How much money can you expect to earn in this period of time? (If you solve this problem with algebra round intermediate calculations to 4 decimal places, in all cases round your final answer to the nearest penny.) Value of investment after 2 years $

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1 answer:

Papessa [141] · Answer 1 · 2022-03-23T09:32:52+03:00

Answer:

Ans. The value of investment after 2 years is $3,155.51

Explanation:

Hi, first we need toconvert that 9.80 percent, compounded quarterly into an effective quarterly rate, that is just by dividing by 4, since there are 4 quarters in a year, that is:

r(effective quarterly)= 9.8%/4 =2.45%

Now, since the rate is effective quarterly, the periods (time of the invesmet) has to be in quarters, so we multiply 2 years by 4 and we get 8 quarters.

With all the above information, we can go ahead and use the following formula in order to find the future value of this investment.

$FutureValue=PresentValue*(1+r)^{n}$

It should all look like this.

$FutureValue=2,600*(1+0.0245)^{8}=3,155.51$

So, the future value of this investment is $3,155.51

Best of luck.