The diffi culty now is to get the n out of the exponent and by itself. This can be accomplished
by using a logarithm:log(5) nlog(1.015)n log(5)
__________log(1.015)n 108.09858293So the term is just over 108 quarters. To convert to years, we must divide by 4 to get a term
of just over 27 years.EXERCISES 3.5
A. Solving for Interest Rate (Annual Compounding)- In Example 3.1.5 we used the Rule of 72 to estimate the rate required for $30,000 to grow to $1,000,000 in 30 years.
Using the techniques of this section, fi nd the effective rate. How good was our estimate? - If Max has $40,057.29 in his investment account, what effective interest rate would he need to earn for this account to
grow to $500,000 in 25 years? - What effective rate does David need to earn on his investments for their value to grow from $594,895 to $1,000,000 in
8 years? - The population of Oakview Junction is now 23,500, and an urban planner has predicted that it will grow to 30,000 in
10 years. What growth rate is assumed in this projection? - What effective rate would you need to earn for $20 to grow to $100,000 in 20 years? In 50 years? In 100 years?
B. Solving for Interest Rate (Nonannual Compounding)- If Silvestre’s account balance grew from $1,595 to $1,703.27 in 3 years, and interest compounded daily, what nominal
rate did the account earn? - What nominal rate, compounded quarterly, would I need to be able to have $21,500 grow to $30,000 in 5 years’
time? - Find the nominal rate compounded monthly that is equivalent to an effective rate of 8.25%.
- A bank advertises an effective rate is 5.35% on a certifi cate of deposit. The interest actually compounds monthly. Find
the nominal rate.
Copyright © 2008, The McGraw-Hill Companies, Inc.
Exercises 3.5 133