Question

What is the effective annual rate of a 12% APR compounded monthly? a. 1% O b. 12.68% O c. 12% O d. 12.12% Your grandmother bought $10,000 of a stock many years ago. The stock is worth $1,000,000 today. If the stock returned 18% annually. approximately how many years ago did she buy the stock? a. 27 b. 28 O c.29 d. 30 How much money would you need to save today if you wish to have $1,000,000 in 20 years and you expect to earn 8% annually? a. S286,546 b. S125.000 c. $214,548 d. 5311.805

Answer 1

1.EAR=[(1+APR/m)^m]-1
where m=compounding periods

=[(1+0.12/12)^12]-1

=12.68%(Approx)

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

1,000,000=10,000*(1.18)^n

(1,000,000/10,000)=(1.18)^n

Taking log on both sides;

log (1,000,000/10,000)=n*log 1.18

n=log (1,000,000/10,000)/log 1.18

=28 years(Approx)

c.Present value=1,000,000*Present value of discounting factor(rate%,time period)

=1,000,000/1.08^20

=1,000,000*0.214548207

=$214548(Approx)