Question

7. All of the following problems involve interest that is being compounded (a) Compute the interest rate needed in order to double an invest- (b) With a 10% interest, how long will it take to triple my initial continuously ment every seven years. investment. (c) Irvin forgot what is the interest rate at his bank. All he knows is that after five years, his initial investment doubled. When will it triple? (Hint: There are two unknowns; one is the interest rate. Whenever there are two unknowns, two equations are needed. So, use the information about money at different times in an appropriate manner.) (d) A person has money withdrawn from his savings account to be placed in his checking account at a continuous basis. This is at a rate of $10,000 a year. This person started with $20,000 placed in the savings account that has a 5% interest. How much will be in the savings account in one year? (Hint: A different expression for the growth of money needs to be derived. So, start with Δ M and, instead of the Eq. 2.4 expression, determine what ΔΜ equals in this setting. Then, solve the equation.)

Answer 1

Answer:

a)

let r be the interest rate.

t=7 years

Initial amount = P

and final Amount = 2P

So for continuous compounding

2P=P*e^(r*t)=P*e^(r*7)

2=e^(r*7)

7r=ln(2)

r=9.90%

B)

given r=10%

Let number of years is t

Initial amount = P

and final Amount = 3P

So for continuous compounding

3P=P*e^(r*t)

e^(10%*t)=3

0.1t=ln(3)

t=11 years

C)

et r be the interest rate.

t=5 years

Initial amount = P

and final Amount = 2P

So for continuous compounding

2P=P*e^(r*t)=P*e^(r*5)

2=e^(r*5)

5r=ln(2)

r=13.86%

Let number of years is t

Initial amount = P

and final Amount = 3P

So for continuous compounding

3P=P*e^(r*t)

e^(13.86%*t)=3

0.1386t=ln(3)

t=7.92 years=8 years