Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt...

Question

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of $10,000 for 5 years at an interest rateof 1.32% if the money isa. compounded semiannually;b. compounded quarterly;c. compounded monthly;d. compounded continuously.

Accepted Answer

Hello. Today we're going to be solving the following problem using the compound interest formula. So the problem states that if $8,000 is deposited into an account with an interest rate of 1.18% compounded quarterly, what is its value after 10 years. While in order to solve this problem, we're going to need to use the compound interest formula which is given to us as a. Is equal to p times the quantity one plus R over N raised to the power of end times T. But what do these variables mean while p is going to be your starting amount or in other words this is your initial investment. R is going to be your interest rate. N is the number of times that interest is compounded and t. Is the total time for the interest and finally a is equal to the total or final amount. And that is what we are looking for in this given problem. So let's take a look at the given information. We are told that $8,000 is deposited into the account or in other words $8,000 is our starting amount. So we're going to let p equal to Next we are told that there is an interest rate of 1.18%. Now that means R is equal to 1.18%. However, we don't want to be working with the percentage, we want to be working with a decimal. So we're going to need to change this percent into a decimal and in order to do that we're going to divide it by 100. This is going to give us the total amount of 0.0118 for interest rate. Next we are told that the interest is compounded quarterly And quarterly means that it is compounded four times out of the year. So N is equal to four. And finally the total time for deposit is going to be 10 years. So T is going to equal to 10. Now we're gonna take our given values and we're gonna plug it into our interest formula. That way we can find the total amount after 10 years. So A is equal to P which is 8000 times the quantity one plus R over N or 0. 8/4 race the power of N which is four times T which is 10. Now we need to go ahead and simplify while one plus 0.1 point 8/4 is going to give us a decimal value of 1.295. So A is equal to Times 1.00295. Raised to the power of four times 10 which is 40. Next this decimal race to the power of 40 is going to give us 1.12505. So A is equal to 8000 times 1.12505. Finally we need to go ahead and multiply these values together and this is going to give you the decimal of 9000.39 or in other words, our final amount after 10 years is going to be $9000 with 39 cents. And this is going to be the answer for the total amount after 10 years. And that means that the solution to this problem is going to be a so I hope this video helps you in understanding how to use the compound interest formula. And I'll go ahead and see you all in the next video.

Key Concepts

Compound Interest

The Compound Interest Formula

Continuous Compounding

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