You just graduated,and you plan to work for 10 years and then to leave for the Australian "Outback" bush country.You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 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 which pays 8 percent compounded annually,what will your financial "stake" be when you leave for Australia 10 years from now?
A) $21,432
B) $28,393
C) $16,651
D) $31,148
E) $20,000

Question

Quizplus · Accepted Answer

To calculate the future value of the savings and the graduation gift, we use the future value formula for a series of cash flows and a single lump sum.1. The $5,000 gift is invested now, so it has 10 years to grow at 8% compounded annually.   Future Value (FV) of the gift = $5,000 * (1 + 0.08)^10 = $10,794.622. For the $1,000 annual savings for the first 5 years, we use the future value of an annuity formula. These savings will have 5 years to grow after the last deposit.   FV of $1,000 savings = $1,000 * [(1 + 0.08)^5 - 1] / 0.08 = $5,866.603. For the $2,000 annual savings for the next 5 years, we use the future value of an annuity formula again. These savings will have no time to grow after the last deposit since it's at the end of the 10 years.   FV of $2,000 savings = $2,000 * [(1 + 0.08)^5 - 1] / 0.08 = $11,733.204. Add the future values together to get the total financial stake:   Total = $10,794.62 (gift) + $5,866.60 (first 5 years savings) + $11,733.20 (next 5 years savings) = $28,394.42The closest answer to our calculation is $28,393, so there might be a slight rounding difference in the calculation process. However, the correct choice based on the closest match is:B

You Just Graduated,and You Plan to Work for 10 Years