136.152: Test #2
20 minutes
Name:_____________________ Student
Number: _______
1. We invest 100 $, with annual interest rate of 6%.
(a) What is the balance after 5 years if the interest is
compounded quarterly? Leave your
answer unsimplified.
(b) What is the balance after 5 years if the interest is
compounded continuously? Leave your answer unsimplified.
(a) Use 
; get 
(b) Use 
; get 
.
2. Solve (in case (a) find the exact solution; in the part (b) leave
your final answer unsimplified):
(a)
(b) 
(a) 
means 
, and this means 
. By a property, the last is true only of 
. We solve this to get
x=2.
(b) We have: 
, so 
, so 
, so 
and so 
.
3. How much do we need to invest if we want to have a balance of 100 000 $
after 5 years under the interest rate of 0.08 compounded continuously? Leave
your final answer unsimplified.
The formula for the balance after t years (with continuously
compounded interest) is 
. We are given that 
, 
and 
. We want to find the initial investment P. So, we need to solve 
, i.e., 
. We get 
.