Question

Unless stated otherwise, interest is compounded annually, and payments occur at the end of the period. Face value for bonds is $1000.

1. Answer the following questions about your vacation package.
   1. You can invest $800 at 12% with quarterly compounding. If you need $1444.90 for the deluxe vacation package, how long would you need to wait for your vacation (in years)?
   2. What is the effective rate on your savings?

Answer 1

a)

Present value = Future value/(1+i)^n

i = interest rate per period

n= number of periods

=>

800 = 1444.9/(1+0.12/4)^n

=>

number of periods n = ln(1444.9/800)/ln(1+0.12/4)

= 20

hence years = 20/12 = 1.67 years

b)

EAR = (1+APR/n)^n - 1

= (1+ 0.12/4)^4 - 1

= 12.55%