Read these directions carefully!! Complete the yellow cells using the function called for in each problem. All answers must be positive numbers. All formulas MUST use cell referencing or no credit will be given! a. Find the FV of $15,500 invested to earn 7.5% after 5 years. Answer this question using the Excel function wizard. Inputs: N = I = PV = 5 7.5% $15,500 Wizard (FV): Note: In the wizard's menu, use zero for PMT because there are no periodic payments. b. Observe how the FV changes at 0%, 5%, and 20% for 0, 1, 2, 3, 4, and 5 years. Years (09): $0.00 0 1 Interest Rate (D10) 0% 5% $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 2 20% $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 3 4 5 FV as function of time and rate $1 $1 $1 $1 $1 $1 SO -0% Future Value - 5% -10% $0 SO SO SO 0 2 5 6 3 Years FV as function of time and rate $1 $1 $1 $1 $1 $1 -0% Future Value -5% +10% $0 $0 $0 $0 0 2 3 4 5 6 Years c. Find the PV of $15,500 due in 5 years if the discount rate is 7.5%. Again, work the problem using the function wizard. Inputs: n = = 5 7.5% $15,500 FV = Wizard (PV): Note: In the wizard's menu, use zero for PMT because there are no periodic payments. d. A security has a cost of $15,000 and will return $20,150 after 8 years. What rate of return does the security provide? Inputs: FV = PV i $20,150 $15,000 ? 8 n Wizard (Rate): Note: Use zero for PMT since there are no periodic payments. Note that the PV is given a negative sign because it is an outflow (cost to buy the security). e. Suppose California's population is 30 million people, and its population is expected to grow by 4% per year. How long would it take for the population to double? Inputs: FV = 60 e. Suppose California's population is 30 million people, and its population is expected to grow by 4% per year. How long would it take for the population to double? Inputs: FV = PV = I = growth rate N = 60 30 4% ? Wizard (NPER): Years to double. f. Find the PV of an annuity that pays $11,000 at the end of each of the next 5 years if the interest rate is 15%. Then find the FV of that same annuity. Inputs: PMT N $11,000 5 15% I PV: Use function wizard (PV) PV = FV: Use function wizard (FV) FV g. How would the PV and FV of the annuity change if it were an annuity due rather than an ordinary annuity? Use the "type" box in the function wizard (omitted or zero for end of period, and one for annuity due) PV annuity due (Use function wizard (PV) = Exactly the same adjustment is made to find the FV of the annuity due. FV annuity due (use function wizard (FV) = h. What would the FV and the PV for problems a and c be if the interest rate were 7.5% with semiannual compounding rather than 7.5% with annual compounding? Part a. FV with semiannual compounding: Inputs: PV = i = Orig. Inputs: $15,500 7.50% 5 New Inputs: $15,500 3.75% 10 n = 1 DIN mon h. What would the FV and the PV for problems a and c be if the interest rate were 7.5% with semiannual compounding rather than 7.5% with annual compounding? Part a. FV with semiannual compounding: Inputs: PV = i = Orig. Inputs: $15,500 7.50% 5 New Inputs: $15,500 3.75% 10 n = Wizard (FV): $0.00 Part c. PV with semiannual compounding: Inputs: FV = Orig. Inputs: $15,500 7.50% 5 New Inputs: $15,500 3.75% 10 n = Wizard (PV): $0.00 i. Find the PV of an investment that makes the following end-of-year payments. The interest rate is 8%. Year 1 Payment $100 $200 $400 2 3 Rate = 8% To find the PV, use the NPV function: PV = j. Suppose you bought a house and took out a mortgage for $150,000. The interest rate is 8%, and you must amortize the loan over 10 years with equal end-of-year payments. Set up an amortization schedule that shows the annual payments and the amount of each payment that goes to pay off the principal and the amount that constitutes interest expense to the borrower and interest income to the lender. Original amount of mortgage: Term of mortgage: Interest rate: $150,000 10 8% j. Suppose you bought a house and took out a mortgage for $150,000. The interest rate is 8%, and you must amortize the loan over 10 years with equal end-of-year payments. Set up an amortization schedule that shows the annual payments and the amount of each payment that goes to pay off the principal and the amount that constitutes interest expense to the borrower and interest income to the lender. Original amount of mortgage: Term of mortgage: Interest rate: $150,000 10 8% Annual payment (use PMT function): Year 1 2 3 4 Observe the amortization of this mortgage Beg. Amt. Pmt Interest Principal End. Bal. $150,000.00 $0.00 $ 12,000.00 -$12,000.00 $162,000.00 $162,000.00 $0.00 $ 12,960.00 -$12,960.00 $174,960.00 $174,960.00 $0.00 $ 13,996.80 -$13,996.80 $188,956.80 $188,956.80 $0.00 $ 15,116.54 -$15,116.54 $204,073.34 $204,073.34 $0.00 $ 16,325.87 -$16,325.87 $220,399.21 $220,399.21 $0.00 $ 17,631.94 -$17,631.94 $238,031.15 $238,031.15 $0.00 $ 19,042.49 -$19,042.49 $257,073.64 $257,073.64 $0.00 $ 20,565.89 -$20,565.89 $277,639.53 $277,639.53 $0.00 $ 22,211.16 $22,211.16 $299,850.69 $299,850.69 $0.00 $ 23,988.06 -$23,988.06 $323,838.75 5 6 7 8 9 10 Extensions: i. This graph shows how the payments are divided between interest and principal repayment over time. Breakdown of payments $30,000.00 $20,000.00 $10,000.00 $- III Principal Interest $(10,000.00) $(20,000.00) $(30,000.00) 1 2 3 4 5 6 7 8 9 10 Years