Question

Jane was born Aug 1st 18 years ago. Her parents contributed $2,000 into a Coverdell Education Savings Account (ESA) at her birth and on her birthday each year. It’s Aug 5th and Jane is ready to withdraw her first tuition payment. If she discovers her ESA is $64,131.91, what was the average rate of return for the investment? Does the question ask or are the payments at the beg(gining) or end of the periods?____________ What unit of time answers the question? _______________ Do I need to convert other variables to the answer’s unit of time? __________ Circle the variable below that answers the question. N = I = PV = PMT = FV =

1. (1pt) You contribute $250.00 per month in to a retirement account. The account averages 5.5% return. Disregarding tax implications, how much do you have in the account at the end of 10 years?

Does the question ask or are the payments at the beg(gining) or end of the periods?____________

What unit of time answers the question? _______________

Do I need to convert other variables to the answer’s unit of time? __________

Circle the variable below that answers the question.

N =

I =

PV =

PMT =

FV =

2. (1pt) You decide to borrow money from Cousin Vinnie and he has agreed to a 20 percent interest rate per year. If you borrowed $200 a year ago, and know you have to pay him in full exactly $716.64 (and make no other payments to him), how long from now until you must pay him back?

Does the question ask or are the payments at the beg(gining) or end of the periods?____________

What unit of time answers the question? _______________

Do I need to convert other variables to the answer’s unit of time? __________

Circle the variable below that answers the question.

N =

I =

PV =

PMT =

FV =

3. (1pt) Five years ago, you bought a piece of art at auction for $1.2 million. Yesterday, you sold that piece at auction for $2,630,937.64. You also purchased a new piece yesterday for $300,000. If the piece you just bought earns the same rate of return as the first one, how much will you be able to sell it for in 8 years?

Does the question ask or are the payments at the beg(gining) or end of the periods?____________

What unit of time answers the question? _______________

Do I need to convert other variables to the answer’s unit of time? __________

Circle the variable below that answers the question.

N =

I =

PV =

PMT =

FV =

Answer 1

(1)

Assuming the payments were made at the end of the period, the time is 19 years ($2000 contributed at birth + $2000 every year thereafter till 18 years). You may draw a timeline to understand this better. The unit of time to be taken is years. The variable that answers the question is I.

N=19 years, PMT=$2000, FV=$64131.91, PV=0, PMT=$2000, I=?

Solving for I, I=5.49% p.a. (a financial calculator or Excel can be used for this, or trial and error method if solved manually)

(2) You contribute $250 per month. Converting years into months, N=10 years or 120 months

N=120, PMT=$250, PV=0, I=5.5% p.a = 5.5%/12 % per month = 0.4583% per month, FV=?

FV= $39,876.90

(3)

I = 20% p.a., PV=$200, FV=$716.64, PMT=0, N=?

Here, N is in years since I is expressed per annum.

Solving for N, N=7 years

Since the question mentions that you borrowed the $200 a year ago, the time remaining until you have to pay him back is 6 years (7 - 1 years)

(4)

For the initial sale, N=5 years, PV=$1,200,000, FV=$2,630,937.64, PMT=0, I=?

Solving for I, I=17%

This is return on your investment in the initial auction.

For the new piece, you target to earn the same return hence I=17%

I=17%, N=8 years, PV=$3,000,000, PMT=0, FV=?

FV=10,534,359.83

You will be able to sell it for $10,534,359.83 assuming you earn a return of 17%.