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Final Exam Study

# Final Exam Study - Question 1 Periodically Compounded...

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Question 1 – Periodically Compounded Investment Suppose that you have available an account that earns 3.65% nominal interest, compounded weekly. 1.1)What is the periodic interest rate, precise to the nearest hundred‐thousandth of a percent? =3.65%/52 = 0.07019% 1.2)If you deposit \$3000 into this account and leave it alone to accrue interest, what will the account be worth after one week? =(3000*0.07019%)+3000 = \$3002.11 1.3)If you deposit \$3000 into this account and leave it alone to accrue interest, what will the account be worth after one year? =(3000* ( 1+0.0365/52 ) ^52 = \$3111.48 1.4)If you deposit \$3000 into this account and leave it alone to accrue interest, what will the account be worth after one decade? =(3000* ( 1+0.0365/52 ) ^ ( 52*10 ) ) = \$4320.99 1.5)What is the APY of this account? =( ( 1+0.0365/52 ) ^52)-1 = 3.716% 1.6)What lump sum should you deposit in this account now if you wish the account to be worth \$6000 after five years? Set up 6 columns: Principal, APR (3.65%), Periodic Rate (0.07019%), Time (5), nper (5*52=260), and FV (=principal*(1+periodic rate)^nper). Goal seek FV by changing the principal. = \$4999.43 1.7)If you deposit \$60 into this account every week (right after the compounding action), what will the account be worth immediately after the 200th deposit? Use the “=FV function” =FV(0.07019%,200,60) = \$12,878.30 1.8)What size should an identical weekly deposit into this account be in order for the account to be worth \$250,000.00 immediately after the 780th deposit? Set up the amortization table (7 rows, see paper) = \$240.85 Question 2 Continuously Compounded Investment Suppose that you have available an account that earns 3.65% nominal interest, compounded continuously. 2.1) If you deposit \$3000 into this account and leave it alone to accrue interest, what will the account be worth after one year? =3000*EXP(3.65%) = \$3111.52 2.2) What is the APY of this account? =( ( 1+0.0365/365 ) ^ ( 365 ) )-1 = 3.717% Question 3 – Periodically Compounded Loans You acquire a loan to help you buy a house. The loan is a 25‐year fixed‐rate mortgage with a nominal interest rate of 5.1%, compounded monthly, with identical monthly payments (made at month end). The amount borrowed is \$345,000. 3.1) What will the size of each monthly payment be? \$2036.99 3.2) How much does the balance of the loan decrease in the first month (after the finance charge and monthly payment are applied)? \$570.74 3.3) What is the baseline total cost of the loan (that is, the projected cost if there are no larger‐than‐ usual payments made during the life of the loan)? \$611,096.16 3.4) What is the balance of the loan at the start of the 120th month? \$256,844.26 Use amortization table for all the above Question 4 – Future Values and Lump Sum Equivalency Scaling based upon an account that earns an annual interest rate of 3.2%, compounded monthly, and considering these assets: --A promissory note worth \$4000 in 7 seven years. --A simple bond which pays the holder \$40 at the end of each month for 100 months.

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Final Exam Study - Question 1 Periodically Compounded...

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