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 given problem using the compound interest formula. So the problem states that if $8000 is deposited into an account with an interest rate of 1.18% compounded semiannually, what is the value after 10 years? In order to solve this problem, we need to make sense of 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 N times T. P. Is going to be your starting amount. R is going to be your interest rate. N is the number of times that interest is compounded and T. Is going to be the total time for our interest. And finally A is going to be the final amount which is what we are looking for in this problem. So let's go ahead and take a look at the given information. We are told that $8000 is deposited into the account. So 8000 is going to be our starting point. So we allow P two equal to 8000 next we are told that the account has an interest rate of 1.18%. So r is equal To 1.18%. But we cannot work with the percentage. We need to change this percent into a decimal. And in order to do that, we're going to go ahead and divide that by 100. This is going to give us an interest rate of 0. next we are told that interest is compounded semiannually. Now the term semiannually means that the interest is going to be compounded twice per year. So N is equal to two. And finally the total amount of time is going to be 10 years. So T is equal to 10. Now what we're going to do is take our given values and plug it into the compound interest formula so we can figure out how much money we are left with after years. So a is equal to P which is 8000 times the quantity one plus R over N. Or one plus 0.118 over N. Which is two raised to the power of N times T, which is two times 10. So now we need to go ahead and simplify well one plus 0.11 8/2 is going to give us the decimal of 1.59. So A is equal to Times 1.0059. And this is going to be raised to the power of two times 10 which is 20. Now 1.0059. Race to the power of 20 is going to give us the decimal of 1.124, So a is equal to Times 1.124854. And finally we just need to multiply 8000 by this decimal which is going to give us the approximate value of 8,998.83. Or in other words, $8,998 with 83 cents is the total amount after 10 years. And this is going to be the answer to this problem. And that means that the solution to this problem is going to be C. 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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