# Quantitative Problem Help

Pls help me solve following problem: In three years, an investor deposits the first of eight \$1000 payments into a special fund. The fund will earn interest at the rate of 5% per year until the end of the fifth year. Thereafter, all money accumulated in the fund will earn a reduced interest rate of 4% compounded annually until the end of the tenth year. How much money will the investor have in the fund at the end of ten years assuming no withdrawals are made?

It helps to draw a timeline for these types of problems to illustrate when cash flows are received(sent) and which rate should be used for which years. The questions doesn’t specify, but assuming each of the next 7 payments are at the start of subsequent years: t=0 1 2 3 4 5 6 7 8 9 10 5% 5% 5% 4% 4% 4% 4% 4% 1K 1K 1K 1K 1K 1K 1K 1K Year 3 1,000^1.05 = 1,050 Year 4 2,050^1.05 = 2,152.50 Year 5 3,152.50^1.05 = 3,310.13 Year 6 4310.125^1.04 = 4,482.53 Year 7 5,482.53^1.04 = 5,701.83 Year 8 6,701.83^1.04 = 6,969.90 Year 9 7,696.90^1.04 = 8,004.78 Year 10 9,004.78^1.04 = 9,364.97

This is uneven CF series The first three years, deposits are annuity due with interest rate of 5% --> FVA(3) = 1000*(1+0.05)^3 = 3310 From year 4th to year 5th is single sum cash flow, interest rate of 5% --> FV(5) = 3310*(1+0.05)^2 = 3649 From year 6th to year 10th is single sum cash flow, interest rate of 4%–> FV(10) = 3649*(1+0.04)^5=4440 Is that right?

Thanks you. But the answer is: 9,251.82. This problem in Schweser Practice Exam 2008.

PMT=1000 N=3 I/Y=5 FV=? FV=3152.5 Clear TVM PV=3152.5 PMT=1000 N=5 I/Y=4 FV=? -> 9251.82

The assumption is not clear “In three years, an investor deposits the first of eight \$1000 payments into a special fund…”, so cannot define cash flow exactly. Gatorwalsh timeline for CF with interest rate of 5% should be t=5. From t=6 the interest rate is reduced to 4%.

@Thu Thuy: I’m Vietnamese too. Can you explain. I also can’t understand the assumption.

Yeah The timeline: t = 0 1 2 3 4 5 6 7 8 9 10 And the deposit begin at t=3, means investor will make payment to investment account at year 3rd From year 3rd to year 5th the interest rate of 5% And from year 6th to 10th the interest rate of 4% The language problem is in the phrase “In the three year” my dear : )

@Thu Thuy:I understanded. This problem may easy if we use English as the first language.

uhm, never get this language mistake again

no problem guys! This was one of the tricky problems we discussed before we wrote the Level 1 Dec exam last year. So I doubt it has much to do with your English skills specifically. A lot of people had trouble interpreting the question. Good luck studying.

I get something slightly different \$5,525.63 5 PAYMENTS TO YEAR3+5 \$3,121.60 3 PAYMENTS TO YEAR3+5+3 \$5,976.52 BRING THIS GUY TO YEAR 3+5+3 \$9,098.12 8 PAYMENTS TO YEAR 3+8 \$9,840.53 FV of all 8 payments to year 3+10

I’m using the HP 12C. I keep getting the wrong answer (should be 3152.5). I cleared the TVM before doing this. Anyone else getting this or know how to fix this? PMT=-1000 N=3 i=.05 FV=? FV=3001.50

I notice that Schweser does a crappy job stating questions. At any rate, when the first payment starts in three years, we are dealing with a regular annuity from the standpoint of t=2. FV of \$1000 per year, N=3, I/R=5 is \$3,152.50. This is calculated at t=5. So we inflate this value by 1.04^5, and that gives us \$3,835.50 in year 10. FV of \$1000 per year, N=5, I/R=4 is \$5,416.32 Add the two and you get \$9,251.82.