Question

Denise has her heart set on being a millionaire. She decides that at the end of every year she will put away $8,000 into her “I want to be a millionaire account” at he local bank. She expects to earn 6% annually on her account. How many years must Denise faithfully put away her money to succeed at becoming a millionaire?

You will receive $3,000 a year, for fifteen years at an opportunity cost of 6%. What is the PVAF?

You invest $450 today in an account that will pay you 5.5% per year. You will not need the money until you take your trip around the world in seven years. What is the FVIF?

What would you pay for the following investment if your opportunity cost of risk is 4.5%? You will receive $770 today, $1,000 in three years, $500 in six years, and after that starting in year seven receive payments of $1,200 a year for ten years.

Answer 1

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

1,000,000=8000*[(1.06)^time period-1]/0.06

1,000,000=133333.333*[(1.06)^time period-1]

[(1.06)^time period-1]=(1,000,000/133333.333)

(1.06)^time period=(1,000,000/133333.333)+1

(1.06)^time period=8.5

Taking log on both sides;

time period*log 1.06=log 8.5

time period=log 8.5/log 1.06

=36.73 years(Approx)

2.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=3000[1-(1.06)^-15]/0.06

=3000*9.71224899

Hence PVAF=9.7122(Approx)

3.We use the formula:  
A=P(1+r/100)^n
where
A=future value
P=present value  
r=rate of interest
n=time period.

A=450*(1.055)^7

=450*1.45467916

Hence FVIF=1.4547(Approx)

4.Present value=Cash flows*Present value of discounting factor(rate%,time period)

=770+1000/1.045^3+500/1.045^6+1200/1.045^7+1200/1.045^8+1200/1.045^9+1200/1.045^10+1200/1.045^11+1200/1.045^12+1200/1.045^13+1200/1.045^14+1200/1.045^15+1200/1.045^16

=$9321.62(Approx)