Tutorial 1 - TVM Part 1 - Extra Problems

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Feb 20, 2024

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CH.5 TVM Part 1 Calculator Resources: http://www.yorku.ca/ntahani/ADMS3530/fincalc.html Extra Review Problems 1. What is the future value of $10,000 on deposit for five years at 6 percent simple interest? (What if it was compounded annually?) A. $7,472.58 B. $10,303.62 C. $13,000.00 D. $13,382.26 FV = PV + (PV x r x t) 2. How much can be accumulated for retirement if $2,000 is deposited annually, beginning one year from today , and the account earns 9 percent interest compounded annually for 40 years? A. $87,200.00 B. $675,764.89 C. $736,583.73 D. $802,876.27 Bonus Question. What is the retirement amount if it begins today? (Bonus question) ANS: What if you do 675,764.89 x 1.09? Remember that annuity due has an extra compounding period. PMT = 2000 N = 40 I/Y = 9 CPT = FV PV = 0 3. How much interest is earned in the third year on a $1,000 deposit that earns 7 percent interest compounded annually? A. $70.00 B. $80.14 C. $105.62 D. $140.00 1000 x (1.07)^2 = 1144.90 after 2 years Take 1144.90 x 0.07 = 80.143 PV x (1+r)^(T-1) Do not do T-1 if this is an annuity due
4. Assume the total expense for your current year in college equals $20,000. Approximately how much would your parents have needed to invest 21 years ago in an account paying 8 percent compounded annually to cover this amount? A. $952 B. $1,600 C. $1,728 D. $3,973 20,000 = x (1.08)^21 X = 3973 FV = 20000 I/y = 8 N = 21 PMT = 0 CPT PV = 3973 Check this PV = 3973 I/y = 8 N = 21 PMT = 0 CPT FV = 20000 5. How long must one wait (to the nearest year) for an initial investment of $1,000 to triple in value if the investment earns 8 percent compounded annually? A. 9 years B. 14 years C. 22 years D. 25 years PV = -1000 FV = 3000 I/y = 8 PMT = 0 CPT N = 14 years approximately 6. A broker tells you, "Give me $5,000 today and I'll return $20,000 to you in five years. To the nearest percent, what annual interest rate is being offered? A. 25 percent B. 29 percent C. 32 percent D. 60 percent PV = 5000 FV = -20000 N = 5
PMT = 0 CPT i/y = 32 percent Bonus question: What would be the effective annual rate (EAR)?: 32 percent 7. What is the present value of the following payment stream, discounted at 8 percent annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3? A. $5,022.11 B. $5,144.03 C. $5,423.87 D. $5,520.00 Formula Method PV = CF/(1+r)^T……. PV = 1000/(1.08)^1+2000/(1.08)^2+3000/(1.08)^3 = 5,022.11 CF method CF0 = 0 CF1 = 1000 CF2 = 2000 CF3 = 3000 NPV - > I = 8 CPT NPV = 5022 8. What is the present value of the following set of cash flows at an interest rate of 7 percent; $1,000 today, $2,000 at end of year one, $4,000 at end of year three, and $6,000 at end of year five? A. $9,731 B. $10,412 C. $10,524 D. $11,524 CF0 = 1000 F=1 for all (If we were getting 1000 for 2 years, F = 2, 3 years F = 3 etc.) CF1 = 2000 CF2 = 0 CF 3 = 4000 CF 4 = 0 CF 5 = 6000 Press “NPV”, I = 7 ENTER, CPT “NPV” 9. How much must be saved annually, beginning one year from now , in order to accumulate $950,000 over the next 10 years, earning 9 percent annually? A. $62,529 B. $63,587 C. $74,500
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D. $84,587 N = 10 I/y = 9 FV = 950000 PV = 0 CPT PMT = 62529 10. Approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8 percent annually, and the first payment occurs one year from now? A. $1,067,000 B. $1,250,000 C. $2,315,000 D. $2,500,000 N = 25 I/y = 8 PMT = 100000 FV = 0 CPT PV = 1,067,000