You just graduated and you expect to work for ten years and then to leave for the Australian "Outback" bush country.You figure you can save $1,000 a year for the first five years and $2,000 a year for the next five years.These savings cash flows will start one year from now.In addition,your family has just given you a $5,000 graduation gift.If you put the gift now and your future savings when they start,into an account that pays 8% compounded annually,what will your financial "stake" be when you leave for Australia 10 years from now.(Round to the nearest whole dollar)
A) $21,432
B) $28,393
C) $16,651
D) $31,148
E) $20,000

Question

Quizplus · Accepted Answer

Step 1 - Calculate the present value of each annuity. PV = PMT × 11ea7fdb_fc1e_4971_a768_55b802736919_TB2902_11 PV = 1,000 × 11ea7fdb_fc1e_4972_a768_1ddd6be89615_TB2902_11 = $3,992.71 Using a financial calculator: N = 5, I = 8, PMT = -1,000, FV = 0, cpt PV = $3,992.71 PV = 2,000 × 11ea7fdb_fc1e_7083_a768_535f72ee74b9_TB2902_11 = $7,985.42 Using a financial calculator: N = 5, I = 8, PMT = -2,000, FV = 0, cpt PV = $7,985.42 Step 2 - Discount the $2,000 annuity back to today from year 5. PV = 11ea7fdb_fc1e_7084_a768_2fb2ea5b3132_TB2902_11 PV = 11ea7fdb_fc1e_7085_a768_771d64ee4ee7_TB2902_11 = $5,434.74 Step 3 - Add all three of the cash flows together, then grow that sum to the end of year 10. 3,992.71 + 5,434.74 + 5,000 = $14,427.45 FV = 14,427.45 × (1.08)¹⁰ = $31,147.79 An alternative method using a financial calculator: Step 1 - Calculate the NPV of the cash flows. CFo = 5,000, C01 = 1,000, F01 = 5, C02 = 2,000, F02 = 5, NPV I = 8, cpt NPV = $14,427.45 Step 2 - Use the NPV as the PV to find the FV of the cash flows. N = 10, I/Y = 8, PV = -14,427.45, PMT = 0, cpt FV = $31,147.79

You Just Graduated and You Expect to Work for Ten