Question

- How many years will it take for $100,000 to grow to $500,000 if it is invested at an annual interest rate of 9.15%? Round to the nearest 0.01.

- You are offered a line of credit with a quoted interest rate of 20% with daily compounding. What is your effective annual interest rate? Round to the nearest 0.01%.

Answer 1

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

500,000=100,000*(1.0915)^n

(500,000/100,000)=(1.0915)^n

5=(1.0915)^n

Taking log on both sides;

log 5=n*log (1.0915)

n=log 5/log (1.0915)

=18.38 years(Approx)

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

=[(1+0.2/365)^365]-1

=22.13%(Approx)