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Date Posted: 14:33:56 04/13/01 Fri
Author: Brian
Subject: Re: TVM Problems
In reply to: Cheryl Saunders 's message, "TVM Problems" on 08:30:41 04/11/01 Wed

The answers I came up with are explained below, but I am not terribly sure of the accuracy of any one of them. If you had the answer key to compare with my answers, we could be more certain. I just wanted to make sure you understood that my answers are by no means the gospel of finance since I am only a student and not even a finance major. If my answers aren't correct, I at least hope they will lead you in the right direction. Please, please, PLEASE consult with your finance professor to verify the answers and methods I have used are correct. I don't want to lead you astray. That being said, here's what I got:

#1 $350,000 loan problem. I used the CF Key. CF0=0, C01=50,000, F01=1, C02=40,000, F02=1. Then, I used teh NPV key and entered I/Y=100% and CPT for NPV. NPV=45,000. I then subtracted the present value of the 4 payments from the $350,000 principal and got $305,000. I then entered negative $305,000 as my PV on my TVM keys, FV=0, I/Y=100, and N=12. I CPT for PMT for the last 12 equal, annual payments. PMT=$305, 074.48

#2 $2,000 deposit problem. I converted the nominal rates you gave me into effective interest rates using the ICONV function. For Bank A, NOM=6.86, C/Y=365, CPT for EFF. EFF=7.10. For Bank D, NOM=6.82, C/Y=5,000(I just picked a very high number since the effective rate ceases to increase at extremely high rates of compounding. CPT for EFF. EFF=7.06. Therefore, I picked Bank A since its effective rate was higher. I then used the TVM keys. PV= -2,000, N=25x365=9125, I/Y=6.86/365=0.01879452, PMT=0, CPT for FV. FV=$11,111.56

#3 I used the TVM keys again. N=10, FV=1,000,000, PMT=0, I/Y=8.25, CPT for PV. PV=$452,606.67

#4 More TVM stuff. PV=472,750, PMT=0, FV=1,000,000, N=10x365=3650, CPT for I/Y. I/Y=0.02035, which is the daily interest rate. Multiply that rate by 365 to get the nominal annual rate. 0.02035x365=7.429%

#5 On this problem, I discounted the $1,000,000 back to January 1st, 2004 (or year 3). 1,000,000/[(1+.09)^(7x2)]. That is (one million) divided by (1.09 to the 14th power). At t=3, the $1,000,000 was worth $299,246.46. Then, I used the TVM keys. PV=250,000, N=6, I/Y=9/2=4.5, FV=299,246.46, CPT for PMT. PMT=$3,918.27 for the 6 equal deposits at 6-month intervals.

#6 I used the TVM keys on this one too. N=32, PV=0, I/Y=8, PMT=250x12=3,000, CPT for FV. FV=$402,640.61


>Would someone provide the correct methods to solve the
>following problems?
>-You want to secure a loan of $350,000. The interest
>rate is 100 percent per year. You offer to make
>payments of $50,000 per year in years 1 and 2 and
>$40,000 per year in years 3 and 4. If the loan is to
>be repaid in 16 years, what is the amount of the 12
>equal payments to be made in each of the last 12
>anniversaries of the loan?
>
>-You are about to deposit $2000 into one of the
>following savings accounts to be left on deposit for
>25 years. Each bank offers an account with a
>different interest rate and compounding period.
>Assuming you want to maximize your wealth, which of
>the following bank accts. would you choose and how
>much money would be in that account in 25 years?
>BankA: 6.86 percent rate compounded daily
>Bank D: 6.82 percent rate compounded continously
>
>For the four following questions, assume you need $1
>million as an ending balance in your account on
>January 1, 2010.
>
>- To achieve your goal, how much would you need to
>deposit on January 1, 2001 into a savings account
>paying 8.25 percent, compounded annually?
>
>- If you had $472,750 on January 1, 2001, what nominal
>interest rate, compounded daily, would you have to
>earn to have the necessary $1,000,000 on January 1,
>2010?
>
>- Assume that to help you achieve $1,000,000 goal, a
>benefactor gives you $250,000 on January 1, 2001. You
>will then make 6 equal additional deposits on each
>June 30, 2001 through 2003 and on each January 1, 2002
>through 2004. If all of this money is deposited in a
>bank account that pays 9 percent p.a., compounded
>semin-annually, how large must your deposits be?
>
>- Compute the future value at the end of year 32 of a
>$250 deposited every month for 32 years (with the
>first deposit made one month from today) into an
>account that pays 8 percent p.a.
>
>Thanks so much

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