Matthews friend Aaron wants to go to business school While h

Matthew\'s friend, Aaron, wants to go to business school. While his father will share some of the expenses, Aaron still needs to put in the rest on his own. But Aaron has no money saved for it yet. According to his calculations, it will cost him $20,885 to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $4,500 at the end of every year in a mutual fund, from which he expects to earn a fixed 10% rate of return. It will take approximately years for Aaron to save enough money to go to business school. 3.40 years 5.40 years 5.00 years 4.00 years Flash Player MAC 30,0,0,134

Solution

1.

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

20885=4500[(1.1)^n-1]/0.1

20885=45000[(1.1)^n-1]

(20885/45000)=(1.1)^n-1

(1.1)^n=0.46411+1

Taking log on both sides;

n*log 1.1=log 1.46411

n=log 1.46411/log 1.1

=4 years(Approx).

2.

Let rate of return be x%

At this rate;present value of payments=3511.1

3511.1=950/1.0x+950/1.0x^2+950/1.0x^3+950/1.0x^4+950/1.0x^5

Hence x=rate of return=11%