Grace's bank has a Cerificate of Deposit with an APR of 5% compounded monthly.(a) If Grace deposits $1000 in the account, what will be the value in 5 years?(b) If Grace needs $10,000 in 5 years, how much should she deposit monthly? **Certificate of Deposit Calculations**Grace's bank has a Certificate of Deposit (CD) with an Annual Percentage Rate (APR) of 5%, compounded monthly.**(a) Future Value Calculation:***Problem:* If Grace deposits $1000 in the account, what will be the value in 5 years?To solve this, we use the future value formula for compound interest:\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]where:- $ A $ = the future value of the investment/loan, including interest.- $ P $ = the principal investment amount (the initial deposit) = $1000.- $ r $ = the annual interest rate (decimal) = 0.05.- $ n $ = the number of times that interest is compounded per year = 12.- $ t $ = the time the money is invested for in years = 5.Plugging in the values, we get:\[ A = 1000 \left(1 + \frac{0.05}{12}\right)^{12 \times 5} \]**(b) Monthly Deposit Calculation:***Problem:* If Grace needs $10,000 in 5 years, how much should she deposit monthly?To solve this, we use the future value of an annuity formula:\[ A = P \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}} \]where:- $ A $ = the future value of the annuity (savings goal) = $10,000.- $ P $ = the monthly deposit amount.- $ r $ = the annual interest rate (decimal) = 0.05.- $ n $ = the number of times the interest is compounded per year = 12.- $ t $ = the number of years = 5.Rearranging the formula to solve for $ P $, we get:\[ P = \frac{A \times \frac{r}{n}}{\left(1 + \frac{r}{n}\right)^{nt} - 1} \]Substituting the known values:\[ P = \frac{10000 \times \frac{0.05}{12}}{\left(1 + \frac{

Here, the formula used is: CI=P1+rnnt Here, CI is compound interest, P is the principal amount, r is…

Grace's bank has a Cerificate of Deposit with an APR of 5% compounded monthly. (a) If Grace deposits $1000 in the account, what will be the value in 5 years? (b) If Grace needs $10,000 in 5 years, how much should she deposit monthly?

Grace's bank has a Cerificate of Deposit with an APR of 5% compounded monthly. (a) If Grace deposits $1000 in the account, what will be the value in 5 years? (b) If Grace needs $10,000 in 5 years, how much should she deposit monthly?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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