Scenario 1. John invests $10,000 in a 3-year CD. The earning is 8% APR compounded monthly. (a) What is the payout when this CD matures? (b) If John wants to double his payout when the 8% APR CD matures, how long should he hold this CD? Solution. CD is a Certificate of Deposit. A CD is a product offered by banks with a premium (higher) interest rate. Once started, the money cannot be withdrawn until the CD matures. Here we have several pieces of information, including the initial investment P= $ interest rate i is % APR, and the term is years. However, the interest is compounded monthly. Therefore, our term lasts for months/year x years months. Furthermore, APR is annual-based; we need to convert it to monthly-based. To do that, we just need to divide the APR by 12, e.g., % APR = %/12 monthly = (fourth decimal point, not in percentage). (a) The payout or future value can be calculated through the formula, F P (1+ i $ ) = $ x (1+ . The interest is F- P = $ (b) To double the payout means our F will be $ P is still = $ and the interest rate is still .We can either start with the formula F = P (1 + i) to derive n, or we can just use the formula n = In (F/ P)/In (1+i) In (F/ P) In ($ )=In (write to the fourth decimal point) = (fourth decimal point) In (1 + i) = In (1 + (write to the sixth decimal point) Therefore n In (F/ P)/In (1+i)= months > years (divided by 12 months/year)
Scenario 1. John invests $10,000 in a 3-year CD. The earning is 8% APR compounded monthly. (a) What is the payout when this CD matures? (b) If John wants to double his payout when the 8% APR CD matures, how long should he hold this CD? Solution. CD is a Certificate of Deposit. A CD is a product offered by banks with a premium (higher) interest rate. Once started, the money cannot be withdrawn until the CD matures. Here we have several pieces of information, including the initial investment P= $ interest rate i is % APR, and the term is years. However, the interest is compounded monthly. Therefore, our term lasts for months/year x years months. Furthermore, APR is annual-based; we need to convert it to monthly-based. To do that, we just need to divide the APR by 12, e.g., % APR = %/12 monthly = (fourth decimal point, not in percentage). (a) The payout or future value can be calculated through the formula, F P (1+ i $ ) = $ x (1+ . The interest is F- P = $ (b) To double the payout means our F will be $ P is still = $ and the interest rate is still .We can either start with the formula F = P (1 + i) to derive n, or we can just use the formula n = In (F/ P)/In (1+i) In (F/ P) In ($ )=In (write to the fourth decimal point) = (fourth decimal point) In (1 + i) = In (1 + (write to the sixth decimal point) Therefore n In (F/ P)/In (1+i)= months > years (divided by 12 months/year)
Intermediate Accounting: Reporting And Analysis
3rd Edition
ISBN:9781337788281
Author:James M. Wahlen, Jefferson P. Jones, Donald Pagach
Publisher:James M. Wahlen, Jefferson P. Jones, Donald Pagach
ChapterM: Time Value Of Money Module
Section: Chapter Questions
Problem 11E
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