Hi,
Can anyone please help to explain this question? I am having a trouble with these kinds of problems.
Gerard Jones plans to save for his 5-year doctorate degree, which starts 6 years from now. The current annual expenditure is USD7,200 and it is expected to grow by 7 percent annually. Gerard will need to make the first payment 6 years from today. He identifies a savings plan that allows him to earn an interest of 8 percent annually. How much should Gerard deposit each year, starting one year from today? Assume that he plans to make 5 payments.
Explanation:
A is correct. This problem can be solved in three steps.
Step 1: Find the annual expenditures
Annual Expendituret=6=7,200 (1+0.07)6=USD10,805
Annual Expendituret=7=7,200 (1+0.07)7=USD11,562
Annual Expendituret=8=7,200 (1+0.07)8=USD12,371
Annual Expendituret=9=7,200 (1+0.07)9=USD13,237
Annual Expendituret=10=7,200 (1+0.07)10=USD14,163
Step 2: Find the present value of annual expenditures at t = 5
Time Period **Annual Expenditure (USD)**Present Value 6 10,805 10,805 (1.08)-1 =10,004 7 11,562 11,562 (1.08)-2 =9,912.5 8 12,371 12,371 (1.08)-3 =9,820.5 9 13,237 13,237 (1.08)-4 =9,729.6 10 14,163 14,163 (1.08)-5 =9,639 SUM = USD 49,106
Step 3: Find the annuity payment
N = 5, %i = 8, PV = 0, FV = 49,106, CPT PMT.
PMT = 8,370.
A USD8,370. B USD8,539. C
USD8,730.